10.19 A playground merry-go-round has a radius of 4.50 m and a moment of inertia

Question

10.19 A playground merry-go-round has a radius of 4.50 m and a moment of inertia of 255 kg*m^2 and turns with negligible friction about a vertical axle through its center. A. A child applies a 25.0 N force tangentially to the edge of the merry-go-round for 18.0 s . If the merry-go-round is initially at rest, what is its angular velocity after this 18.0 s interval? B. How much work did the child do on the merry-go-round? C. What is the average power supplied by the child?

Explanation / Answer

F = I*alpha =>alpha = F/I = (25/255) and w_o = 0 rad/s we know that w = w_o + alpha*t t = 18 sec => w = 18*(25/255) = 1.765 rad/s.....angular velocity after this 18.0 s interval B)teta = 0.5*((25/255)^2)*(18^2) = 1.557 radians = 0.496 revolutions 1 revolution => S = 2*pi()*4.5 0.496 revolutions => S = 0.496*2*pi()*4.5 work done = F*distance = 25*0.496*2*pi()*4.5 = 350.346 J C)Average power = W/t = 19.464 W

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