Pe Notes on Bimechanics

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Conservation of linear momentum when both objects are moving * In conservation of linear momentum the momentum of both objects before impact is not lost but remains the same for the combined momentum of both objects after impact. Example

When playing snooker, once struck, the white “cue ball” will contain a certain amount of momentum. This is determined by its mass and how fast its travelling. When this ball makes contact with the black ball the total momentum of the two balls before and after collision will remain the same. Some of the momentum would have simply transferred from the white ball to the black ball.

Impulse-momentum relationship
* Impulse (FXt) is the product of force and time. That is, how much force can be produced over a time interval. This impulse is then directly responsible for creating momentum (changing momentum from zero), changing momentum (increasing momentum in a slow jog to that required for a sprint) or stopping momentum (catching a ball). * The impulse needed to stop the momentum of a falling gymnast is constant; it is the time and therefore the peak force that may be altered. That is, the area under the impulse curve stays the same irrespective of whether you land in a foam pit or concrete – it is the shape of the curve that changes.

* Therefore the longer the force can be applied to an object and the greater the size of the force applied, the greater the object’s impulse!
Coefficient of Restitution
* The COR is the ratio of the velocities after compared with before an impact, and this value will change for different impact situations. * Rebound to the same height or with same velocity (e.g. collision during game of pool) = Coefficient of 1; perfectly elastic collision. * No rebound = Coefficient of 0; perfectly inelastic collision. * Rebound to a lesser height =Value >0 and <1; imperfectly inelastic collision. This is the most common in sporting activities. For example, best shown by the decreasing height of a ball dropped onto a hard surface. * A number of factors alter the COR:

* Impact Surfaces
* Heat of colliding objects
* Velocity of the colliding objects.
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* Tennis ball rebound higher from a `hard court` than a grass court`. New tennis ball has grater elasticity than an old one and will therefore bounce higher and return to its original position quickly. Better for Tennis player because they can generate more velocity when racket collides with a new ball!

Moment of Inertia
* Moment of inertia is all about:
* The size or mass of an object (related to inertia), and * The distribution of mass about an axis of rotation (centre of mass, grip on implement or external point of rotation, such as a gymnast holding onto to a high bar and performing a swing). Angular Momentum

* Moment of inertia and angular velocity interrelate in aerial movements because angular momentum is constant when an athlete is off the ground, or near to constant when on a surface with low friction such as an ice rink or dance floor. * This relationship between moment and angular velocity is based on Newton’s 1st Law: ‘A body will rotate about its axis with constant angular momentum, unless acted upon by an external force’. * As angular momentum is constant when airborne, moment of inertia and angular velocity are inversely proportional. As one increases the other decreases. Example

Diver - From the time the diver leaves the board to the time he enters the water, his angular momentum will be conserved as no external forces are acting on him. At the commencement of the dive, his body position is very open, resulting in a large moment of inertia and low angular velocity. As the diver moves into a “tuck” position, he decreases his moment of inertia and increases his angular...
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