b. Consider a wheel initially at rest and rotating at 30 rev/min, for this process the wheel done 5500 J work. What are the moment of inertia and angular momentum of the wheel?

Question

5b) Consider a wheel initially at rest and rotating at 30 rev/min, for this process the wheel done 5500 J

work. What are the moment of inertia and angular momentum of the wheel?

Answer 1

I do not understand the phrase "for this process the wheel done 5500 J work".

A wheel does not do work, a force does work.

So I will answer the question under the assumption that

"for this process 5500 J of work was done without any friction".

This work then gave the wheel 5500 J of rotational energy.

Let

f = 30 min^-1 = 0.5 s^-1 be the frequency of the wheel,

w = 2πf = π s^-1 be the angular velocity,

E = 5500 J be the rotational energy of the wheel,

I be the moment of inertia,

L be the angular momentum

The formula for rotational energy is

E = Iw²/2

Therefore

I = 2E/w² = 2×5500/π² = 1114.5 kgm²

The formula for angular momentum is

L = Iw = 2E/w = 2×5500/π = 3501.4 kgm²/s