A wheel rotating about a fixed axis has a constant angular acceleration of 4.0 rad/s2. In a 4.0-s interval the wheel turns through an angle of 80 radians. Assuming the wheel started from rest, how long had it been in motion at the start of the 4.0-s interval? a. 3 s.
b. 6 s.
c. 9 s.
d. 12 s.

a. 3 s.

Explanation:

Given;

angular acceleration of the wheel, α = 4 rad/s²

time of wheel rotation, t = 4 s

angle of rotation, θ = 80 radians

Apply the kinematic equation below,

Given initial angular velocity, ω₀ = 0

Apply the kinematic equation below;

Therefore, the wheel had been in motion for 3 seconds.

a. 3 s.