Solve This Physics Problem

Question

A flywheel slows from 643 rev/min to 427 rev/min while rotating through 53 revolutions. (a) What is the angular acceleration (in rad/s^2) of the flywheel? (Assume the flywheel is rotating in the positive direction. Indicate the direction with the sign of your answer.) (b) How much time elapses (in s) during the 53 revolutions?

Answer 1

One of the equations of motion for circular motion is:

where ωf is the final angular velocity (in radians/sec), ωi is the initial angular velocity (in radians/sec), α is the angular acceleration (in radians/sec²), and "θf - θi" is the final angle minus the initial angle or "the number of radians of motion traveled"

Convert 643 rev/min to radians/sec:

643 rev/min x (2π radians)/(1 rev) x (1 min)/(60 sec) = 67.335 radians/sec

Convert 427 rev/min to radians/sec:

427 rev/min x (2π radians)/(1 rev) x (1 min)/(60 sec) = 44.715 radians/sec

Convert 53 rev into radians:

53 rev x (2π radians)/(1 rev) = 333.009 radians

44.715² = 67.335² + 2α(333.009)

1999.46 = 4533.98 + 666.018α

-2534.51 = 666.018α

α = -3.8055 rad/sec² or, rounded to 2 sig figs, α = -3.8 rad/s²

Another of the kinematic equations is:

Now that you know α, you can solve for time (t)

44.715 = 67.335 + (-3.8055)t

solve for t