An electric motor is attached to a small wheel that is rotating at a rate of 150 rev \min . if the motor is switched off so that it has a negative angular acceleration of 2.2 rad\s^2 , how long dose it take the wheel to stop? And how many revolutions has the wheel turned during this time interval ?

Answer 1

First, we need to convert the initial rotation rate to radians per second:
150 rev/min * 2π rad/rev * 1/60 min/s = 15.7 rad/s

Next, we can use the formula for angular acceleration to find the time it takes for the wheel to stop:
ωf = ωi + αt
0 = 15.7 rad/s - 2.2 rad/s^2 * t
t = 7.14 s

Finally, we can use the formula for angular displacement to find how many revolutions the wheel has turned during this time interval:
θ = ωit + 1/2 αt^2
θ = 15.7 rad/s * 7.14 s + 1/2 (-2.2 rad/s^2) * (7.14 s)^2
θ = 55.9 rad
55.9 rad * 1 rev/2π rad = 8.9 rev (rounded to one decimal place)

Therefore, the wheel takes 7.14 seconds to stop and has turned 8.9 revolutions during that time interval.