Question

You need to design an industrial turntable that is 48.0 cm in diameter and has a kinetic energy of 0.210 J when turning at 45.0 rpm (rev/min).

a. What must be the moment of inertia of the turntable about the rotation axis?

b. If your workshop makes this turntable in the shape of a uniform solid disk, what must be its mass?

Answer 1

Sol::
Given::

Diameter(D)= 0.48 m
Radius(r)= 0.24 m
Kinetic energy(KE)= 0.210 J
w= 45.0 rpm (rev/min).

ω = 45 rev/min * 2π rad/rev * 1min/60s
= 4.712 rad/s

A)
We have

KE = ½Iω²
0.210 J= 0.5 * I * (4.712 rad/s)²

I = 0.0189 kg·m²

(b)

I = ½mr²
0.0189 kg·m² = ½ * m * (0.24 m)²
m= 0.656 Kg

Hope this answer helps you
Hope will get the VOTE
Thank you