Question 8.13: WARMING UP GOAL Find a moment of inertia and apply the rotat...
WARMING UP
GOAL Find a moment of inertia and apply the rotational analog of Newton’s second law.
PROBLEM A baseball player loosening up his arm before a game tosses a 0.150-\mathrm{kg} baseball, using only the rotation of his forearm to accelerate the ball (Fig. 8.27). The forearm has a mass of 1.50 \mathrm{~kg} and the length from the elbow to the ball’s center is 0.350 \mathrm{~m}. The ball starts at rest and is released with a speed of 30.0 \mathrm{~m} / \mathrm{s} in 0.300 \mathrm{~s}. (a) Find the constant angular acceleration of the arm and ball. (b) Calculate the moment of inertia of the system consisting of the forearm and ball. (c) Find the torque exerted on the system that results in the angular acceleration found in part (a).
STRATEGY The angular acceleration can be found with rotational kinematic equations, while the moment of inertia of the system can be obtained by summing the separate moments of inertia of the ball and forearm. The ball is treated as a point particle. Multiplying these two results together gives the torque.
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