Question

Problem #3 A thin disk begins to rotate from rest with a constant angular acceleration. The disk takes 1.2 sec to make its second complete revolution. Find: (a) the time in sec) it took the disk to make its first revolution; (b) the angular acceleration (in rad/sec) of the disk.

Answer 1

here,

time taken for second complete rotation , t2 = 1.2 s

let the time taken to first complete revolution be t1 and angular acceleration be alpha

for first revolution

theta1 = w0 * t1 + 0.5 * alpha * t1^2

2pi = 0 + 0.5 * alpha * t1^2 ......(1)

for two revolution

theta2 = w0 * (t2 + t1) + 0.5 * alpha * (t1 + t2)^2

2 * 2pi = 0 + 0.5 * alpha * (t1 + 1.2)^2 ......(2)

from (1) and (2)

t1 = 2.9 s

alpha = 1.5 rad/s^2

a)

the time taken to first complete revolution is 2.9 s

b)

the angular acceleration is 1.5 rad/s^2