Question

Chapter 10 Problem 010: Starting from rest, a disk rotates about its central axis with constant angular acceleration. In 7.00 s, it rotates 18.1 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 7.00 s? (d) With the angular acceleration unchanged, through what additional angle (rad) will the disk turn during the next 7.00 s?

Answer 1

Total distance travelled, = 18.1 rad
Time taken, t = 7 s
Consider the angular acceleration as and the initial angular velocity, i = 0

a)
Using the equation, = i t + 1/2 t²
18.1 = 0 + 0.5 x x 7²
= 0.739 rad/s²

b)
Total distance travelled, = 18.1 rad
Total time taken, t = 7 s
Average angular velocity = /t
= 18.1/7
= 2.586 rad/s

c)
Initial angular velocity, i = 0
Consider f as the final angular velocity after time t = 7 s.

Using the formula, f = i + t,
= 0 + 0.739 x 7
= 5.171 rad/s

d)
Now the initial angular velocity is the instantaneous angular velocity in the previous part.
i = 5.171 rad/s
Time taken, t = 7 s
Distance travelled,
= i t + 1/2 t²
= 5.171 x 7 + 0.5 x 0.739 x 7²
= 54.3 rad