4. In softball, the pitcher throws with the arm fully extended (straight at the

Question

4. In softball, the pitcher throws with the arm fully extended (straight at the elbow). In a fast pitch the ball leaves the hand with a speed of 90 km/h. Find the rotational kinetic energy of the pitcher's arm given its moment of inertia is 0.720 kg. m^2 and the ball (m=0.156 kg) leaves the hand at a distance of 0.600 m from the pivot at the shoulder.( hint K=1/2Itot omega^2, Itot = Iarm + Iball) A. 273 J B. 312 J C. 674 J D. 868 J E. 625 J 5. Suppose you start an antique car by exerting a force of 300 N on its crank for 0.250 s. What angular momentum is given to the engine if the handle of the crank is 0.300 m from the pivot and the force is exerted to create maximum torque the entire time? (in kg m^2/s A. 360 B. 90.0 C. 30.0 D. 25.5 E. 22.5 6. A playground merry-go-round has a mass 120 kg and a radius 1.80 m and it is rotating with an angular velocity of 0.50 rev/s. What is its angular velocity after a 22.0 kg child gets onto it by grabbing its outer edge? (Assume that there is no lost angular momentum and the child is initially at rest). A. 0.27 rev/s B. 0.36 rev/s C. 0.50 rev/s D. 0.88 rev/s E. 0.42 rev/s

Explanation / Answer

KE = 0.5*I*w^2 = 0.5*I*(v/l)^2 = (0.5*0.72*25*25)/(0.6*0.6) = 625 J

option E

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5)

L = r*F = 0.3*300 = 90.0

+++++

6)

I1 = 0.5*M*R^2 = 0.5*120*1.8*1.8 = 194.4 kg m^2

w1 = 0.5rev/s

Li = I1*w1

I2 = m*R^2 = 22*1.8*1.8 = 71.28

Lf = (I1+I2)*w2

L2 = L1

w2 = (I1*w1)/(I1+I2) = (194.4*0.5)/(71.28+194.4)

w2= 0.36 rev/s

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