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If a ball is incident obliquely on a horizontal surface and is allowed to bounce more than once, then it is likely to bounce many times before it starts rolling along the surface. The number of bounces before rolling commences depends on the initial vertical speed and the normal coefficient of restitution. The transition from bouncing to rolling is examined using a simple theoretical model and is compared with experimental data obtained by filming the process with a video camera. We find that the final rolling speed is proportional to the initial horizontal speed of the ball and depends on the initial ball spin, but is independent of the tangential coefficient of restitution. Representative videos for different balls are included as supplementary material, including a superball thrown with a backspin that creates a back and forth motion. Instructors could use the experiment and/or analysis for an advanced undergraduate lab or use a simplified observational exercise for non-majors. Editor's Note: When a ball is dropped on a horizontal surface with no initial spin, previous studies have found that its bouncing behavior can be simply described using a coefficient of restitution, which gives the ratio of the velocity after the bounce to before the bounce. The value of this coefficient is −1 for a perfectly elastic ball/surface, with a smaller magnitude for any real ball. In many sports, like golf, basketball, or bowling, balls are thrown at an angle and are often given some initial spin by the player. Depending on initial conditions, these balls can bounce, roll, or start by bouncing and then transition to rolling. Here, the transition from bouncing to rolling is shown to be described by using both a vertical and horizontal coefficient of restitution, with the horizontal velocity defined at the spinning edge of the ball rather than its center. Videos of undergraduate level experiments are included, with results used to validate the model. [ABSTRACT FROM AUTHOR]

(1) and (2) need to be solved numerically to find I y i and I F i vs. time, for given values of I k i SB 1 sb , I k i SB 2 sb , I c i , I m i , and I v i SB 0 sb . An interesting question is whether these and other balls store all the initial impact energy as elastic energy when they compress, or whether they lose some of that elastic energy while they are compressing as well as during the expansion stage. The maximum total elastic energy is 0.82 I E i SB 0 sb , so not all of the initial kinetic energy is stored as elastic energy; 82% of the initial kinetic energy is stored as elastic energy at maximum ball compression, and then 82% of the stored elastic energy is returned as kinetic energy when the ball bounces off the surface. The area under the curve while I y i increases represents the energy required to compress the ball, and the area under the curve while I y i decreases represents the energy recovered while the ball expands. [Extracted from the article]

Li et al. conducted an experiment on the bounce of a capsule dropped vertically onto a horizontal surface. They found that if the capsule has spin, it can bounce to a slightly greater height than the drop height. This is because rotational kinetic energy is converted to vertical translational kinetic energy during the bounce. The effect is more pronounced when the capsule is incident obliquely with spin. Similar effects have been observed with other elongated objects, such as a spinning plastic egg or two golf balls joined together. This phenomenon can be visually appealing and is often used in lecture demonstrations. [Extracted from the article]

Measurements are presented on oblique angle collisions between two identical balls, each suspended as pendulum bobs. If one ball is at rest and is struck by the other ball incident without spin at an oblique angle, then both balls spin in the same direction after the collision. The results can be explained in terms of friction between the balls. At glancing angles, the balls slide throughout the collision. At other angles of incidence, the balls initially slide, then grip, and then slide again when the balls release their grip. The collision can be described in terms of two different coefficients of restitution: one involving the normal incident and post-collision speeds and the other involving the tangential speeds of the contact points before and after the collision. The coefficient of restitution and the collision time vary with the collision speed but remain relatively constant if the speed changes by a factor less than about two. [ABSTRACT FROM AUTHOR]

This article discusses the concept of the quality factor, Q, in damped oscillatory motion. The quality factor is a measure of the energy loss per cycle and can be calculated by plotting oscillator amplitude vs. time or by counting the number of observed cycles. The article provides examples of simple harmonic motion, such as a pendulum and a mass on a spring, and explains the equation that describes their motion. It also explains how the amplitude of the oscillation decreases exponentially with time due to damping and how the quality factor is related to the energy loss. The article suggests that counting the number of cycles can be a simple and quick method to estimate the quality factor of a damped oscillation. [Extracted from the article]

This article discusses a claim made in a previous journal article about kinetic energy conservation in elastic collisions. The authors of the current article argue that the coefficient of restitution (COR) should be defined in terms of the normal components of the incoming and outgoing speeds of the objects at the point of impact, rather than just the translational motion. They argue that this definition would result in a COR of unity in a perfectly elastic collision, regardless of the point of impact. The issue of impact point dependence is recognized by U.S. Major League Baseball, which specifies the performance of baseball bats in terms of the COR at the point of impact. [Extracted from the article]

When a short rod collides end-on with a long rod, kinetic energy is not conserved since the longer rod vibrates after the collision. In theory, the fractional energy loss is equal to 1 âˆ' L 1/ L 2 where L 1 is the length of the short rod, L 2 is the length of the long rod, and the long rod is initially at rest. Measurements of the energy loss are presented for a set of steel rods and a set of wood dowels. The steel rods were shorter than the dowels and behaved more like steel balls, with only a small decrease in kinetic energy. A larger fractional energy loss was observed when using the dowels since a larger fraction of the initial kinetic energy was converted to vibrational energy in the dowels. In neither case was the energy loss equal to 1 âˆ' L 1/ L 2. [ABSTRACT FROM AUTHOR]

The normal coefficient of restitution (COR) for a sphere that bounces obliquely or at right angles on a horizontal surface usually has an approximately constant value between 0 and 1, which are the limits for a completely inelastic or a perfectly elastic collision respectively. Different results are obtained for the bounce of a non-spherical object. Measurements are presented for a double sphere consisting of two golf balls joined together, incident obliquely on a smooth horizontal surface. The COR varied from 0.15 to 1.0 depending on the alignment of the two balls and the incident spin. The results are explained in terms of a simple bounce model where the lower ball slides on the horizontal surface, and in terms of three different values of the COR defined in terms of (a) the bounce height, (b) the vertical speed of the contact point and (c) the ratio of the final to the initial kinetic energy. [ABSTRACT FROM AUTHOR]

A simple experiment is described concerning the vertical bounce of a nonspherical object. The object consisted of two golf balls joined together. The balls were dropped onto a heavy, rigid horizontal surface and were filmed with a video camera to measure the coefficient of restitution (COR). For spherical objects, the COR is usually defined in terms of the vertical speed of the centre of mass and can vary between zero and unity depending on the elastic properties of the object and the surface on which it bounces. For nonspherical objects, the COR is best defined in terms of the vertical speed of the contact point. For the two golf balls, the centre of mass COR was found to vary between −4 and +2 depending on the incident spin and the angle of inclination of the long axis. The contact point COR was found to be 0.8 ± 0.2, regardless of the incident spin and angle of inclination. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The impact of a ball with a flexible beam is analysed both experimentally and theoretically. The impact generates a bending wave that may or may not return to the impact point before the ball bounces off the beam. If the ball rebounds before the bending wave returns, then the rebound speed of the ball is determined by localised bending of the beam in the vicinity of the impact point. For a short duration impact, the rebound speed is therefore independent of whether the beam is freely supported or clamped at one or both ends, unless the impact occurs close to an end of the beam. Two different values of the coefficient of restitution can be defined, depending on whether the speed of the beam is measured when the ball rebounds or at a later stage. Experimental results were obtained using a small rubber ball impacting light wood and steel beams. A video camera and two piezoelectric disks were used to capture the relevant ball speeds and vibration response of the beam. The experiment would be suitable for undergraduate students. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Experimental results are presented concerning the impact of a 20 mm steel ball incident obliquely on a smooth granite surface. The angle of incidence and the spin of the ball were varied to examine the effects on the rebound velocity and spin. If the ball is incident with topspin, there is only a small change in the horizontal speed of the ball, in which case the effective coefficient of friction between the ball and the surface is relatively small. If the ball is incident without spin or with backspin there is a large reduction in the horizontal speed of the ball. The results can be described by a simple model where the coefficient of friction remains constant if the ball slides throughout the impact or where the tangential coefficient of restitution remains constant if the ball grips the surface. Unlabelled Image • The oblique bounce of a steel ball is consistent with simple impact models. • The ball slides at large angles of incidence with a coefficient of friction about 0.13. • The ball grips at small angles of incidence with a tangential coefficient of restitution about 0.45. • With sufficient topspin there is no sliding phase. • With sufficient backspin there is no grip phase. [ABSTRACT FROM AUTHOR]

The article studies the physics and geometry behind the unusual bounce of an oval shaped football. Compared to a spherical ball, an oval shaped ball that is thrown diagonally on the ground can bounce either backwards or forward with or without rotation and can spin either way. Formulas such as the coefficient of restitution, simple bounce formula and measurements of both vertical and oblique drops are explained.

The article describes a method for measuring the speed and bounce of tennis courts which was developed based on filming the bounce of a tennis ball with a standard, 25 frames per second (fps), video camera. It discusses the results obtained at both 25 fps and 500 fps and some of the physics issues involved in interpreting the data. The precautions needed to obtain valid results and the International Tennis Federation's (ITF) procedure of classifying and testing court surfaces are also noted.

The article discusses the intrinsic power and swing speed of different sports equipment in relation to their inertial properties. It is stated that the performance of a sports equipment is dependent on both the equipment's intrinsic property and its swing speed. Also explained is the importance of the moment of intertia (MOI) and coefficient of restitution to the performance of sports equipment.

Tennis courts are normally classified as fast or slow depending on whether the coefficient of sliding friction (COF) between the ball and the surface is respectively small or large. This classification is based on the fact that the change in horizontal ball speed is directly proportional to the COF if the ball is incident at a small angle to the horizontal. At angles of incidence greater than about 16° it is commonly assumed that the ball will roll during the bounce, in which case one can show that the ratio of the horizontal speed after the bounce to that before the bounce will be 0.645 regardless of the angle of incidence or the speed of the court. Measurements are presented showing that (a) at high angles of incidence, tennis balls grip or 'bite' the court but they do not roll during the bounce, (b) the bounce:speed ratio can be as low as 0.4 on some courts and (c) the normal reaction force acts through a point ahead of the centre of mass. An interesting consequence is that, if court A is faster than court B at low angles of incidence, then A is not necessarily faster than B at high angles of incidence. An exception is a clay court which remains slow at all angles of incidence. The measurements also show that the coefficient of restitution for a tennis ball can be as high as 0.9 for an oblique bounce on a slow court, meaning that the ball bounces like a superball in the vertical direction and that slow courts are fast in the vertical direction. [ABSTRACT FROM AUTHOR]

Ivchenko recently provided a simple mathematical description and a nice animation of a ball colliding head-on with two other balls at rest but connected by a spring.[1] He was interested primarily in calculating the amount of energy lost due to vibration of the second pair of balls. In effect, he assumed that the coefficient of restitution was unity to calculate the ball speeds immediately after the initial collision, then found that the coefficient of restitution was less than unity due to the subsequent energy loss. That is, what is the value of the coefficient of restitution I e i for a collision between two balls if energy is lost I after i the collision rather than during the collision?. [Extracted from the article]

The article offers information on a physics experiment conducted to enhance the coefficient of restitution (COR) and the spin of a golf ball. It mentions that the experiment measure the rotation angle and the average angular velocity of the ball. It says that surface compression and elastic energy are dependant on the ball and surface stiffness. It states that friction causes the ball to rotate and elastic energy innate in the surface if the ball is rigid than the bounce surface.