Question

A disk with mass m = 11.8 kg and radius R = 0.31 m begins at rest and accelerates uniformly for t = 17.2 s, to a final angular speed of ω = 31 rad/s.

1.What is the angular acceleration of the disk?

2.

What is the angular displacement over the 17.2 s?

3.

What is the moment of inertia of the disk?

4.

What is the change in rotational energy of the disk?

Answer 1

here,

the mass of disk , m = 11.8 kg

the radius of disk , r = 0.31 m

the time taken , t = 17.2 s

the final angular speed , w = 31 rad/s

a)

let the angular acceleration be alpha

using first equation of motion

w = w0 + alpha * t

31 = 0 + alpha * 17.2

solving for alpha

alpha = 1.8 rad/s^2

the angular acceleration is 1.8 rad/s^2

b)

the angular displacement , theta = w0 * t + 0.5 * alpha * t^2

theta = 0 * t + 0.5 * 1.8 * 17.2^2 rad

theta = 266.3 rad

c)

the moment of inertia of disk , I = 0.5 * m * R^2

I = 0.5 * 11.8 * 0.31^2 kg.m^2

I = 0.57 kg.m^2

d)

the change in rotational energy of the disk , KE = 0.5 * I * w^2

KE = 0.5 * 0.57 * 31^2 J

KE = 273.9 J