Question

Starting from rest, a disk rotates about its central axis with constant angular acceleration. In 2.00 s, it rotates 44.3 rad. During that time, what are the magnitudes of (a) the angular acceleration and (b) the average angular velocity? (c) What is the instantaneous angular velocity of the disk at the end of the 2.00 s? (d) With the angular acceleration unchanged, through what additional angle (rad) will the disk turn during the next 2.00 s?

Answer 1

here,

time , t = 2 s

theta = 44.3 rad

let the average accelration be alpha

a)

theta = w0 * t + 0.5 * alpha * t^2

44.3 = 0 + 0.5 * alpha * 2^2

alpha = 22.15 rad/s^2

b)

the average angular velocity , w = theta /t

w = 44.3 /2 = 22.15 rad/s

c)

at t = 2 s

the instantaneous angular velocity , w' = 0 + alpha * t

w' = 0 + 22.15 * 2

w' = 44.3 rad/s

d)

the angle covered in next 2 s , theta' = w'* t + 0.5 * alpha * t^2

theta' = 44.3 * 2 + 0.5 * 22.15 * 2^2

theta' = 132.9 rad