Question

In: Physics

A machine begins to apply an equal torque to two cylinders of equal mass and equal...

A machine begins to apply an equal torque to two cylinders of equal mass and equal radius R, so that they begin to rotate about their central axis (the line shown here). One cylinder is solid. The other cylinder is a thin-walled hollow cylinder. After a certain amount of time, what statement can be made about the rotary motion of the cylinders?

Question 14 options:

a)

The cylinders rotate at the same speed.
b)

This solid cylinder rotates at twice the speed of the thin walled hollow cylinder.
c)

This thin-walled hollow cylinder rotates at twice the speed of the solid cylinder.
d)

Not enough information is given. We would need to know the numerical value of torque and the time elapsed.

Solutions

Expert Solution

Moment of inertia of a solid cylinder of Radius R about its central axis Is = MR2 / 2

Moment of Inertia of a thin walled hllow cylinder of radius R   Ih = MR2

Torque Where alpha is the angular acceleration

if ah and as are the angular accelerations then

Ih * ah = Is * as

Hence the solid cylinder will rotate with twice the speed of the hoolw cylinder

genius_generous answered 2 years ago
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