Question

You get a great summer job working on the COD grounds crew and have been assigned the task of trimming the lawn around the sign out on Fawell. Because you're the junior person on the crew, you been given one of those older mowers you have to start by pulling on a cord. To start the lawn mower, you must pull on a rope wound around the perimeter of a 5.2kg flywheel. After you pull the rope for 0.88 s, the flywheel is rotating at 4.4 revolutions per second, at which point the rope disengages. This attempt at starting the mower does not work, however, and the flywheel slows, coming to rest 0.25 s after the disengagement. Assume constant acceleration during both spin up and spin down.

1)

Determine the average angular acceleration during the 0.88-s spin-up.

rad/sec²

2)

Determine the average angular acceleration during the 0.25-s spin-down.

rad/sec²

3)

What is the maximum angular speed reached by the flywheel?

rad/sec

4)

Determine the ratio of the number of revolutions made during spin-up to the number made during spin-down.

Answer 1

1) while spinning up

wi = 0

wf = 4.4*2*pi rad/s = 27.65 rad/s

angular acceleration, alfa_up = (wf - wi)/t

= (27.65 - 0)/0.88

= 31.4 rad/s^2

2) while spinning down

wi = 27.65 rad/s

wf = 0

alfa_down = (wf - wi)/t

= ( 0 - 27.65)/0.25

= -111 rad/s^2

3) maximum angular speed of the wheel, w_max = 27.65 rad/s

4) during spin up,

theta_up = wi*t + 0.5*alfa_up*t^2

= 0 + 0.5*31.4*0.88^2

= 12.16 rad

during spin down,

theta_down = wi*t + 0.5*alfa_up*t^2

= 27.65*0.25 + 0.5*(-111)*0.25^2

= 3.44 rad

so, theta_up/theta_down = 12.16/3.44

= 3.53