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 1.77 rad/s? (Assume the merry-go-round is initially at rest.)

s

(b)

How many revolutions must he go through to generate this velocity?

revolutions

(c)

If he exerts a slowing force of 330 N at a radius of 1.30 m, how long (in s) would it take him to stop them?

s

Explanation / Answer

here,

moment of inertia , I = 84.4 kg.m^2

angular accelration , alpha = 4.44 rad/s^2

a)

final angular speed , w = 1.77 rad/s

let the time taken be t

w = w0 + alpha * t

1.77 = 0 + 4.44 * t

solving for t

t = 0.4 s

b)

the angle covered , theta = w^2 /2alpha

theta = ( 1.77)^2 /(2 * 4.44)

theta = 0.35 rad

the number of revolutions , n = theta/2pi

n = 0.056 rev

c)

F = 330 N , r = 1.3 m

let the angular accelration be alpha'

F * r = alpha' * I

330 * 1.3 = alpha' * 84.4

solving for alpha'

alpha' = 5.08 rad/s^2

let the time taken be t'

0 = w + alpha' * t'

0 = 1.77 - 5.08 * t'

solving for t'

t' = 0.35 s

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