A small, solid cylinder with mass 4 kg and radius 5 cm starts from rest and rota

Question

A small, solid cylinder with mass 4 kg and radius 5 cm starts from rest and rotates without friction about an axis through its center of mass. The rotation axis is fixed so that the center of mass of the cylinder does not move as the cylinder rotates. A string is wrapped around the circumference of the cylinder and is pulled using a constant force F=7 N.

There is a non-zero net torque on the cylinder, but the net force on the cylinder is zero. And The cylinder will undergo angular acceleration but not linear acceleration.

1) What is the moment of inertia of the cylinder? (kg m^2)

2) What is the magnitude of the torque on the cylinder from the force due to the string? (Nm)

3) What is the magnitude of the angular acceleration of the cylinder? (rad/ s^2)

4) What is the angular velocity, , of the cylinder after the force has been pulling for 8 seconds? (rad/ s^2)

5) What is the magnitude of the work done by the string on the cylinder during the first 8 seconds? (J)

Explanation / Answer

1. For a solid cylinder,

I = 1/2mr² = 1/2 * 4kg * (0.05m)² = 0.005 kg·m²

2.

= F * r

= 7N * 0.05m

= 0.35 N·m

3. = / I

= 0.35/0.005

70rad/s²

4. = *t

=70*8

=560 rad/s

5. work done = KE

= 1/2I² =

1/2 * 0.005kg·m² * (560rad/s)²

=784J  

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