Question

2) A solid sphere with mass 2kg and radius 0.2 meters is rotating clockwise about its center with ωi =5 rad/s. a) Find its Moment of Inertia. b) We want to double its angular speed in 3 full turns of the sphere. Find its acceleration. c) A constant force is acting on the edge with 135 degrees angle. Find the Force needed to for this acceleration

Answer 1

PART A:

The moment of inertia of the solid sphere is about its center is

So, the moment of inertia of the sphere is 0.032 kg.m^2.

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PART B:

The initial angular velocity of the sphere is

The final angular velocity is

The angular displacement is

We know

So, the angular acceleration of the sphere is 1.99 rad/s^2.

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PART C:

The torque required for this acceleration is

The torque is given by

So, the force needed for this acceleration is 0.45 N.