A wheel, starting from rest, rotates with a constant angular acceleration of 2.80 rad/s2. During a certain 5.00 s interval, it turns through 65.0 rad. (a) How long had the wheel been turning before the start of the 5.00 s interval? (b) What was the angular velocity of the wheel at the start of the 5.00 s interval?

a) time t1 = 2.14s

b) initial angular speed w1 = 6 rad/s

Explanation:

Given that;

Initial Angular velocity = w1

Angular distance = s = 65 rad

time = t = 5 s

Angular acceleration a = 2.80 rad/s^2

Using the equation of motion;

s = w1t + (at^2)/2

w1 = (s-0.5(at^2))/t

Substituting the values;

w1 = (65 - (0.5×2.8×5^2))/5

w1 = 6rad/s

Time to reach w1 from rest;

w1 = at1

t1 = w1/a = 6/2.8 = 2.14s

a) time t1 = 2.14s

b) initial angular speed w1 = 6 rad/s

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