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A loop-the-loop experiment usually involves a ball rolling around a vertical loop. A different version of the experiment is described where a nut was allowed to slide around a vertical loop. In both experiments there is a large decrease in kinetic energy when the ball or the nut first enters the loop.

A loop-the-loop experiment is described to show how sliding friction affects motion of the ball. Conservation of energy can be used to explain the basic physics, but significant energy loss is observed in practice and expands the usefulness of this apparatus as a teaching tool.

Experimental results are presented concerning the motion of a ball that bounces up an incline a few times then bounces back down again. The number of bounces up the incline is typically small since the speed of the ball in a direction parallel to the incline decreases rapidly, not only during each bounce but also while the ball is in the air. The ball heads back down the incline when it is incident at right angles to the incline.

A collision of one object with two or more objects is relatively complicated in general, but a simple example is provided by Newton's cradle since all the objects are identical and in line. In the present paper, an experiment is described where a heavy mallet collides head-on with two billiard balls. The two conservation equations indicate that many different outcomes are possible. The experimental results are surprising but can be explained in terms of the relative mass and stiffness of the mallet and the balls.

A 2.7 m long stringless pendulum was set up to measure the coefficient of rolling friction of various balls, at higher rolling speeds than usually observed with a short stringless pendulum. The arrangement is easy to set up and makes an impressive classroom demonstration as well as an interesting laboratory experiment.

Measurements and calculations are presented showing how the trajectory of an object sliding across an inclined plane varies with the launch and incline angles. The trajectory depends on the magnitude and direction of the sliding friction force. The experiment is easy to set up, can be analysed using a video camera, and would be suitable for a student experiment or demonstration.

The trajectory of a ball rolling across an inclined plane was recorded on video film to determine if it followed a parabolic path as others have suggested. The challenges in this case were (a) to determine the magnitude and direction of the friction force on the ball, (b) to determine the effect of the friction force on the trajectory and (c) to explain why the rotation axis of the ball rotates as it rolls up and down the incline. The experiment is a simple extension of standard inclined plane experiments but with the extra pedagogical feature that angular velocity sometimes needs to be treated as a vector quantity.

The trajectory of a ball in air is affected by aerodynamic drag and lift. In general, the trajectory needs to be calculated numerically since the acceleration varies with time in both the horizontal and vertical directions. If the trajectory remains approximately parabolic, then simple analytical solutions can be found, giving useful insights into the behavior of the ball as it travels through the air.

If a ball rolls in a circular path on a horizontal surface at constant speed then its horizontal rotation axis changes direction with time. A simple experiment is presented showing that the torque applied to the ball is equal to the rate of change of its angular momentum, even though the magnitudes of its angular velocity and angular momentum remain constant in time.

Calculations are presented showing that the usual 'faster than g' demonstration has a surprising property. That is, a rod hinged at its bottom end rotates at an exponentially increasing rate until it falls with maximum vertical acceleration, unlike an object that falls freely by gravity alone. If the rod is hinged at its top end and released from a horizontal position, then the vertical acceleration is a maximum at the instant it is released.

Oblique angle collisions of two penny coins on a smooth, horizontal surface were filmed with a video camera to investigate the physics of the collision process. If one of the coins is initially at rest, then the two coins emerge approximately at right angles, as commonly observed in billiard ball collisions and in puck collisions on an air table. The coins actually emerged at an angle less than 90 degrees due to friction between the coins, which also resulted in both coins rotating after the collision. At glancing angles, the friction force was due to sliding friction. At other angles of incidence the coins gripped each other and the friction force was then due to static friction.

If an empty coffee cup is spun on a horizontal surface about a vertical axis in an anti-clockwise direction, then the whole cup rotates slowly backwards, in a clockwise direction, about a vertical axis located outside the cup. Clues to this curious behaviour are presented by comparing it with other spinning objects.

A solid ball placed on a rotating turntable is known to roll slowly around a circular path, at a speed 3.5 times slower than the turnable itself. If the ball is located in a straight track across a diameter of the turntable, then it accelerates rapidly to the edge. Both effects were filmed in slow motion using a video camera and a cake decoration turntable, and are presented as supplementary videos. The results agree well with calculations based on rolling motion of the ball.

The coefficient of restitution (COR) for a collision is usually a number between 0 and 1 depending on whether the collision is completely inelastic, or perfectly elastic or something in between. That is the usual situation for colliding spheres or a ball dropped on a horizontal surface. A different situation arises when a bat collides with a ball. A simple experiment is described where a rod is dropped on another rod at right angles. In that case, two different values of the COR can be defined.

Experimental results are presented on the collision of a superball with two different wood blocks. The results are in reasonable agreement with a simple collision model where kinetic energy is conserved, but better agreement is obtained if a small loss of kinetic energy is assumed, as observed. The physics is slightly more complicated than the standard head-on collision of two balls studied in elementary mechanics since it involves rotation as well as translation of one or both of the colliding objects.

A common procedure when conducting physics experiments is to repeat a measurement several times to calculate the mean and standard deviation. That might be the only instruction we give to students as a means to minimize random errors. However, that technique does not guarantee that the answer will be correct. It might give the same wrong answer every time. How then can we teach students to avoid systematic errors? We don't focus on that problem enough when teaching physics. Part of the problem is that we and the students usually know the correct answers in advance, since student experiments have usually been repeated thousands of times by others.

If a smooth ball is dropped vertically without spin on a smooth horizontal surface then one might expect the ball to bounce vertically without spin. If it does not then the centre of mass of the ball does not coincide with its geometric centre. An experiment is described where a billiard ball and a superball are deliberately biassed by adding a small steel ball on one side. The results agree well with theoretical calculations.

Experimental results are presented concerning a bead sliding on a rotating, horizontal rod. If the rod rotates at constant angular velocity then the sliding speed in the radial direction increases exponentially with time, provided that the rotation speed is sufficient to overcome friction. Otherwise the bead rotates in a circular path of constant radius.

Points near the top end of a falling rod hinged at its bottom end can fall faster than g. If a rod falls on a frictionless surface then the bottom end slides backwards and the centre of mass falls vertically with acceleration less than g. The effect was simulated by mounting a rod on wheels and filming the result with a video camera. The experiment provides an example of accelerated motion where the acceleration increases with time.

An experiment is described where a billiard ball and a golf ball were projected with backspin on a horizontal surface to measure the transition from sliding to rolling. During both phases, the torque on the ball is affected by an offset in the line of action of the normal reaction force.

A standard problem for physics students is to calculate or measure the acceleration of an object down an inclined plane. Additional information can be obtained by measuring the angular acceleration as well as the linear acceleration. An experiment is described where a billiard ball was filmed as it rolled down an inclined plane at different inclination angles. The transition from rolling without slipping to rolling with slipping was identified, and the relevant friction coefficients were measured independently from the linear and angular accelerations.

A hula hoop rotating around a person's waist is an example of circular motion where the centripetal force on the hoop is directed towards the centre of the circle rather than the centre of the hoop. The friction force on the hoop is relatively small by comparison since the hoop rolls around the waist. A slight complication is that the hoop rotates in an elliptical path if the waist rotates back and forth in a straight line or if the waist rotates in an elliptical path. Three simple experiments are described to illustrate the physics involved.

A simple experiment for students is to measure the coefficient of restitution (COR) for a vertical bounce on a horizontal surface. In this paper, measurements are presented of the COR for a tennis ball bouncing at an oblique angle on a horizontal surface. Changes in the horizontal and rotation speeds were also measured, by filming the bounce with a video camera. A measurement of this type involves a more extensive examination of basic mechanics, since the friction force acting at the bottom of the ball acts to change both the horizontal speed of the ball and its rotational velocity. The COR for an oblique bounce was found to be larger than that for a vertical bounce and was also found to depend on the incident spin of the ball.

What happens when a perfectly elastic ball collides with a completely inelastic ball? It is shown that the outcome depends on the stiffness of each ball. A standard textbook problem in mechanics is to calculate the outcome of a head-on collision between two balls using conservation of momentum and kinetic energy. It is easily shown that the outcome depends on the relative mass of the balls and their initial speeds. In practice, there is always a net loss of kinetic energy during a collision, which can be expressed in terms of the coefficient of restitution (COR) for the collision. The COR is defined as the relative speed of the two balls after the collision divided by the relative speed before the collision. In a perfectly elastic collision the COR is unity. In a completely inelastic collision, the COR is zero.

The impact force and duration when one billiard ball collides head-on with another is estimated by assuming that the balls are connected by a spring. The results are compared with a measurement when a billiard ball collides with a heavy, rigid surface.

A standard physics experiment for students is to measure the terminal velocity of an object in air or in glycerine. A more difficult challenge is to measure the terminal velocity in water since the depth of the water needs to be large or the object needs to be dropped in the water at a speed close to its terminal velocity. Results obtained by filming the fall in a fish tank are presented for a range of different spheres, showing how the terminal velocity depends on the density of the sphere and its radius. The results provide a useful measurement of the drag force and the drag coefficient for a sphere in water. An additional experiment to measure the Magnus force is described where a ball was spinning when it entered the water.

A well known physics problem is to calculate the friction forces required to support a ladder against a wall. A more tractable problem is to calculate the friction forces needed to support an inclined beam on a ball or a cylinder. In the latter case there are three rather than two points of sliding support. Measurements and calculations are presented to show that a ball can support an inclined beam without slipping, provided the incline angle is not too large.

Two balls on an incline can remain at rest if friction between the balls prevents them rolling down the incline. Results with various balls are presented to show how ball mass, diameter and friction affects the outcome. A stack of four identical balls is also examined.

A ball at rest on a surface can be made to bounce up by pushing it down then releasing the downward force as fast as possible. Measurements and calculations are presented to show how it can best be done.

A method is described to measure the coefficient of restitution (COR) by dropping a ball on a piezoelectric disk. Multiple bounces can be observed at small drop heights, so the average COR over say ten bounces can be obtained from just one ball drop, without having to measure the bounce height or the bounce speed. The results show directly that the maximum impact force on the ball during each bounce decreases linearly with time until the ball stops bouncing.

If a ball rolls at constant speed on a horizontal surface about a horizontal axis then the angular velocity is easily measured. If the ball is projected with additional spin about the vertical axis, then the rotation axis is tilted and it is more difficult to measure the rotation speed. A few examples are presented to show how the separate topspin and sidespin components can be measured.

A spinning top with a spherical bottom end was constructed to examine its behaviour. Experimental results were consistent with theoretical predictions.

When a ball bounces obliquely on a horizontal surface, the bottom of the ball stretches horizontally and then vibrates backward. The resulting ball spin depends sensitively on the transverse vibration frequency. A simple model is presented to describe the effect, showing how the stored elastic energy can result in additional spin.

A simple throwing task is described to illustrate various aspects of projectile motion. The task was to throw a tennis ball in a waste paper bin about 2 m away. Success depends on skill, but it also depends on the physics of the problem. If the ball is thrown underarm, then success depends primarily on the throw speed, which must be controlled to within about 2%. The launch angle can be chosen within a wide range. If the ball is thrown overarm, then the launch angle is just as important as the throw speed.

When a hard object rolls on a soft surface, or vice versa, rolling friction arises from deformation of the soft object or the soft surface. The friction force can be described in terms of an offset in the normal reaction force or in terms of energy loss arising from the deformation. The origin of the friction force itself is not entirely clear. It is investigated qualitatively in this paper by rolling a steel ball on soft foam and by rolling a foam cylinder on a hard surface. The deformation of the foam was observed visually, providing simple insights into the origin of the friction force.

A ball that rolls without sliding down an inclined plane requires a small static friction force to prevent the ball sliding down the incline. The magnitude of that force is investigated by considering the force needed to prevent the contact point from slipping.

Three simple experiments are described using a small water bottle with two holes in the side of the bottle. The main challenge is to predict and then explain the observations, but the arrangements can also be used for quantitative measurements concerning hydrostatic pressure, Bernoulli's equation, surface tension and bubble formation.

A well-known physics demonstration is to pull a tablecloth rapidly from under some crockery without disturbing the crockery. An interesting question is whether the same result can be expected if the crockery is replaced by a ball, given that the ball might roll backwards on the tablecloth. Theoretical and experimental results are presented showing that the result depends on the acceleration of the tablecloth. If crockery is at rest on a tablecloth, and if the tablecloth is pulled slowly, then the crockery will move at the same speed as the tablecloth. With a rapid pull, the crockery appears not to move at all. In fact, the crockery will move a small distance horizontally since the coefficient of sliding friction is not zero. The secret of success is to minimize the horizontal impulse, not by reducing the friction force but by reducing the time over which it acts.

A simple experiment is described to measure the coefficient of rolling friction for a low bounce ball rolling on a horizontal surface. As observed previously by others, the coefficient increased with rolling speed. The energy loss due to rolling friction can be explained in terms of the measured coefficient of restitution for the ball, meaning that low bounce balls have a higher coefficient of rolling friction than high bounce balls.

The acceleration of a vehicle or a bicycle is commonly used in elementary physics courses to illustrate problems concerning Newton's laws of motion when friction forces are involved. The maximum possible acceleration is rarely discussed, although it is of interest to consumers and racing car enthusiasts, and it is sometimes questioned by students. It is the main focus of the present article and is considered from a basic physics point of view, appropriate for classroom discussion.

When measuring the speed of an object with a video camera, a correction may be needed for the time taken by the camera to acquire the image in each frame. Examples are given where the correction is quite significant.

An ice hockey player can strike a puck at speeds up to about 45 m/s (100 mph) using a technique known as the slap shot. There is nothing unusual about the speed, since golf balls, tennis balls, and baseballs can also be projected at that speed or even higher. The unusual part is that the player strikes the ice before striking the puck, causing the stick to slow down and to bend. There appears to be a significant advantage in hitting the ice before hitting the puck, otherwise hockey players would have learned from experience not to do that. In order to investigate the physics of the problem, the authors set up a simple experiment using a flexible meterstick to simulate a real hockey stick and mounted it as a pendulum so it could swing about an axis near the top end. The results presented in this paper support the fact that hockey players know what they are doing when they slap the ice, even though the result appears at first sight to violate conservation of energy.

The act of swinging an object such as a hammer or a tennis racket involves the application of forces and torques in a manner that is intuitively obvious to the person performing the task, but is probably much less obvious to the average physics student. This article describes the basic mechanics of the problem.

Almost everyone will have observed a spinning coin fall to a shuddering stop. How and why does it do that? Several experiments are described, suitable for a student project, to help motivate an understanding of the rotational dynamics involved.

On July 19, 1969, Senator Edward Kennedy drove his vehicle off a low bridge on Chappaquiddick Island in Massachusetts. The vehicle sank in 2.1 m of water, coming to rest on its roof. According to Kennedy's version of events, he managed to escape from the submerged vehicle without injury, but his female companion, Mary Jo Kopechne, drowned without any sign of injury. He did not report the accident to police until 10 hours later. Kennedy's version of the events was widely disbelieved but was never seriously challenged by the local police or accident investigators or at the subsequent inquest. The accident effectively put an end to Kennedy's bid for the presidency of the United States. At least a dozen books have been written on the subject, offering alternative explanations but the physics of the accident itself has never been properly investigated. In this paper, experiments using a toy vehicle are described where the vehicle was projected into a container of water to investigate how the roof may have been damaged. The trajectory through the water was filmed and is explained in terms of elementary physics. Further investigation could be the subject of student projects and would provide an interesting introduction to forensic physics.

Measurements are presented on the rise of a spinning egg. It was found that the spin, the angular momentum and the kinetic energy all decrease as the egg rises, unlike the case of a ballerina who can increase her spin and kinetic energy by reducing her moment of inertia. The observed effects can be explained, in part, in terms of rolling friction between the egg and the surface on which it spins. (Contains 1 table and 7 figures.)

The nature of the drag force on an object moving through a fluid is well documented and many experiments have been described to allow students to measure the force. For low speed flows the drag force is proportional to the velocity of the object, while at high flow speeds the drag force is proportional to the velocity squared. The basic physics depends on whether the flow around the object is laminar or turbulent. It is difficult to observe the flow in a student laboratory, although a dye can be injected into the flow of water for demonstration purposes. An alternative method is described in this paper that allows both the drag force and the initial flow pattern to be measured easily. The technique is simply to film an object when it is dropped into a tank of water. The results can be spectacular when filmed in slow motion, adding to the interest in the experiment itself. The results are directly relevant to the problem of calculating the impact force on an object that falls into water. Water is not as hard as concrete, but it can still exert a large force if the object (or a person) impacts at high speed.

A spinning top or a spinning hard-boiled egg is fascinating to observe since both objects can remain upright for a relatively long time without falling over. If spun at sufficient speed on a horizontal surface, the spin axis rises to a vertical position and the bottom end tends to remain fixed in position on the surface. If the initial spin is insufficient, then the spin axis will not rise all the way to the vertical, in which case a spinning top or a spinning egg will precess slowly around a vertical axis. If the bottom end is rounded, as it is with an egg or with a top having a round rather than a pointed peg, then the vertical precession axis does not necessarily pass through the center of mass. Instead, the precession axis may be located several centimeters away from the center of mass, depending on the radius of the bottom end. As a result, the whole egg or the whole top then rolls along the surface in an approximately circular path, several centimeters in diameter. The essential physics is described in Ref. 1 and the references therein, and in the many more books and papers since the early 1900s quoted in each of the references therein.

The PhiTOP® (or FTOP®) is a physics toy designed not only to act as a spinning top but also to appeal to the eye and to the scientifically curious mind.1 It is currently made in two versions, one from solid aluminum and the other solid brass. Each top is highly polished, and is elliptical in one cross section and circular in another. Its name derives from the ratio of the lengths of the major to minor axes, which is equal to the golden mean F = (1+ v5)/2~1.618. It functions in the same way as a spinning egg or a spinning football in that it rises on one end if it is initially set spinning at sufficient speed with its long axis horizontal. The center of mass rises in an unexpected and somewhat mysterious manner, an effect that it also shares with a tippe top.

The effect of the aerodynamic drag force on an object in flight is well known and has been described in this and other journals many times. At speeds less than about 1 m/s, the drag force on a sphere is proportional to the speed and is given by Stokes' law. At higher speeds, the drag force is proportional to the velocity squared and is usually small compared with the gravitational force if the object mass is large and its speed is low. In order to observe a significant effect, or to measure the terminal velocity, experiments are often conducted with very light objects such as a balloon or coffee filter or muffin cup, or are conducted in a liquid rather than in air. The effect of the drag force can also be increased by increasing the surface area of the object.