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WilkinzMicawber

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- Thread starter WilkinzMicawber
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In summary: However, if the linear velocity is too high, the contact will not be sufficient to transfer the rotational energy, and the ball will not rebound.

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WilkinzMicawber

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Cutter Ketch

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x = sqrt(m/k) v0

The force from the first contact to maximum compression is -k x, so the acceleration is

a = - kx/m.

dx^2/dt^2 = -kx/m

Implies

x = C sin(sqrt(k/m) t)

Which knowing the max x from above must be

x = sqrt(m/k) v0 sin( sqrt(k/m) t)

where t=0 gives x=0 as the moment of initial contact. Maximum compression is reached when

sqrt(k/m) t = pi / 2

So tmax = sqrt(k/m) pi/2

So higher initial velocity gives greater compression but the time of contact is the same.

Regarding the effect that has on the transfer of the angular momentum for some of the time the ball slips and there is one torque then it sticks. Since the force is higher the torque is higher but once it's enough to stop the ball I suppose there isn't much difference if you go to yet higher velocity. I have no idea at what velocity the spin finally stops.

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WilkinzMicawber

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Linear velocity is the speed at which an object is moving in a straight line. In the case of spinning objects, it refers to the speed at which the object is moving around its axis of rotation. The faster an object spins, the higher its linear velocity will be.

The linear velocity of a spinning object has a direct impact on its rebound. The higher the linear velocity, the greater the force of the rebound will be. This is because the object has more kinetic energy, which is transferred into the rebound upon impact.

Yes, the linear velocity of a spinning object can be changed. It can be altered by changing the speed at which the object is spinning or by changing the size of the object. Both of these factors will affect the object's linear velocity.

The surface on which a spinning object rebounds can impact its linear velocity. For example, a smoother surface will result in less friction and therefore a higher linear velocity. A rougher surface will cause more friction, resulting in a lower linear velocity.

Yes, there is an optimal linear velocity for maximum rebound. This will vary depending on the size and weight of the spinning object, as well as the surface it is rebounding from. Generally, a higher linear velocity will result in a stronger rebound, but there may be a point where the object becomes too difficult to control at high speeds.

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