Question

A rotating wheel requires 7.00 s to rotate 28.0 revolutions. its angular velocity at the end of the 7.00-s interval is 96.0 rad/s. what is the constant angular acceleration (in rad/s) of the wheel?

Answer 1

We know: θ = ωo t + 1/2*α*t^2

so, α = 2*(θ - ωo t ) / t^2
Given: angular velocity = 96.0 rad/sectime = 7 secangular distance travelled = 28 rev
We know, In one revolution it completes 360 degrees = 6.28319 radangular distance traveled = 28 rev * 6.28319 rad
So, angular acceleration = 2*(28*6.28 - 96*7) / 7^2 = -20.25 rad/sec^2