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Rolling of round objects down an incline and torque

Q#1
Explain (a) how it is possible for a large force to produce only a small or even zero, torque, and (b) how it is possible for a small force to produce a large torque.

q#2
A hoop, a solid cylinder, a spherical shell, and a solid sphere are placed at rest at the top of an incline. All the objects have the same radius. They are then released at the same time. What is the order in which they reach the bottom? Justify your answer

Solution Preview

q#1
Explain (a) how it is possible for a large force to produce only a small or even zero,
torque, and (b) how it is possible for a small force to produce a large torque.

Torque = F * d where d is the perpendicular distance from the force to the pivot. Torque is proportional to this distance d.

(a) For a large force, reducing the distance d, will produce a smaller torque. When d = 0, torque = 0
(b) For a small force, increasing the distance d, will produce ...

Solution Summary

I have shown how to derive an expression for the velocity of a cylinder, spherical shell, hoop and solid sphere at the bottom of an incline. I have shown, using physics principles, which object will reach the bottom at first. I also have discussed about the torque produced by a large force.

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