Question

Consider a father pushing a child on a playground merry-go-round. The system has a moment of inertia of 84.4 kg · m². The father exerts a force on the merry-go-round perpendicular to its radius to achieve an angular acceleration of 4.44 rad/s².

(a). How long (in s) does it take the father to give the merry-go-round an angular velocity of 2.33 rad/s? (Assume the merry-go-round is initially at rest.)

(b). How many revolutions must he go through to generate this velocity?

(c). If he exerts a slowing force of 290 N at a radius of 1.25 m, how long (in s) would it take him to stop them?

Answer 1

given
I = 84.4 kg.m^2
wo = 0 rad/s
alfa = 4.44 rad/s^2

a) let t is the time taken.

use, t = (w - wo)/alfa

= (2.33 - 0)/4.44

= 0.525 s <<<<<<---------------------Answer

b) angular displacement during this time,

theta = wo*t + (1/2)*alfa*t^2

= 0 + (1/2)*4.44*0.525^2

= 0.6189 radiands

= 0.6189/(2*pi)

= 0.0985 revolutions <<<<<<---------------------Answer

c) angular acceleration during slow down,

alfa' = net torque/I

= -290*1.25/84.4

= -4.295 rad/s^2

let t is the time taken to stop.

use, t = (wf - w)/alfa'

= (0 - 2.33)/(-4.295)

= 0.542 s <<<<<<<<<<---------------------Answer