Question

A cyclist accelerates from rest. After 7 s, the wheels have made 2 revolutions.

a. What is the angular acceleration of the wheels?

b. What is the angular velocity of the wheels after 7 s?

Answer 1

Note: we need to do part b first

b. The average angular velocity is 2*(2pi) rad / 7 s = 4*pi / 7 rad/s = 1.8 rad/s
That is the average. The question did not say, but we have assume the acceleration was constant. So the velocity, at t=7 s, is
2*1.8 rad/s = 3.6 rad/s

a. Now that we know angular velocity, w, at 7 s, angular acceleration, alpha, is
alpha = (change in w)/time = 3.6 rad/7 s = 0.51 rad/s^2

Answer 2

a. V = 2rev/7s * 6.28rad/rev = 1.79 rad/s.
V = a * t = 1.79.
a*7 = 1.79,
a = 0.256 rad/s^2.

b. V = 1.79 rad/s.(see part a).