Question

Suppose the mass of the ball is 60 g and it is spinning at 40 rad/s at a distance of 1.5 m from the center of rotation. The force is 1800 N and it’s applied for 2 ms. Your goal is to find the final angular speed of the tennis ball.

i. What is the initial angular momentum of the tennis ball? Hint: 40 rad/s is the angular speed (?), NOT the linear speed (?). If the angular speed is 40 rad/s and the radius is 1.5 m, what is the linear speed of the tennis ball?

ii. What is the magnitude of the torque caused by the force?

iii. What is the magnitude of the final angular momentum of the tennis ball? The time matters!

iv. What is the final angular speed of the ball?

C. Suppose that instead of hitting the ball forward, the person hits it in a downward direction as shown. This will cause a change in angular momentum ?? in the:

i. x direction iv. – x direction ii. y direction v. – y direction iii. z direction vi. – z direction Hint: What is the direction of the torque caused by the force F?

Answer 1

initial angular momentum = mr² = 0.06*1.5*1.5*40 = 5.4 Kgm²/s

torque = force * distance = 1800*1.5 = 2700Nm

final angular momentum = initial angular momentum + impulse = 5.4+1800*0.002 = 9 Kgm²/s

final angular speed = angular momentum / moment of inertia = 9 Kgm²/s / 0.06*1.5*1.5 = 9/0.135 = 66.66rad/s

C) since the image is not given to get the torque direction required apply right hand thumb rule about center