Consider a father pushing a child on a playground merry-go-round. The system has

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 1.33 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 270 N at a radius of 1.20 m, how long (in s) would it take him to stop them?

Explanation / Answer

Given that

initial angular velocity is wi = 0 rad/s

alpha = 4.44 rad/s^2

I = 84.4 kg m^2

wf = 1.33 rad/sec

then

alpha = (wf-wi)/t

t = (wf-wi)/alpha = (1.33-0)/4.44 = 0.3 sec

b) using theta = (wi*t)+(0.5*alpha*t^2)

theta = (0*t)+(0.5*4.44*0.3^2) = 0.2 rad

then revotions are 0.2/(2*3.142) = 0.0318 rev

c) Torque is T = I*alpha

r*F = I*alpha

1.2*270 = 84.4*alpha

alpha =(1.2*270)/84.4 = 3.84

(w/t) = 3.84

1.33/t = 3.84

t = 1.33/3.84 = 0.346 sec

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