Question

A wheel starts from rest and rotates with constant angular acceleration and reaches an anaular speed of 12 rad/s in 3 s. Find (a) the magnitude of the angular acceleration of the wheel and (b) the angle (in radian) through which it rotates in this time.

Answer 1

(a) 4 rad/s^2

(b) 18 rad

Step-by-step explanation:

w0 = 0, w = 12 rad/s, t = 3 s

(a) Let α be the angular acceleration.

w = w0 + α t

12 = 0 + 3 α

α = 4 rad/s^2

(b) Let θ be the angle rotated

θ = w0 t + 1/2 α t^2

θ = 0 + 0.5 x 4 x 9

θ = 18 rad