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.) 0.300 Correct: Your answer is correct. s (b) How many revolutions must he go through to generate this velocity? 0.0317 Correct: Your answer is correct. revolutions (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? 0.894 Incorrect: Your answer is incorrect. s

Explanation / Answer

here,

c)

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

applied force , F= 270 N

r = 1.2 m

let the angular accelration for slowing be alpha

alpha * I = - F * r

alpha = - 270 * 1.2/(84.4) rad/s^2

alpha = - 3.84 rad/s^2

initial velocity , w0 = 1.22 rad/s

let the time taken to stop be t

w = w0 + alpha * t

0 = 1.22 - 3.84 * t

t = 0.32 s

the time taken is 0.32 s

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