Sample Angular Kinematics Problems
1. A lacrosse player swings his stick of radius 1.6 m at an angular velocity (w) of 345º/s. What is the linear velocity of the ball?
2. When kicking a soccer ball, a player accelerates (a) her lower leg at 4.5 radians/s2 for 0.8 s. If the final angular velocity (wf) of her leg was 1.4 radians/s, what was the initial angular velocity (wi) of her leg?
3. A golfer swings his club of radius 1.2 m at an angular velocity (w) of 340º/s. What is the linear velocity of the club head? What is the linear velocity of the club head if the radius is 0.8 m?
4. When throwing a javelin, a track athlete with a linear velocity of 6.4 m/s, an arm length of 1.2 m and angular velocity (w) at the shoulder of 2.5 radians/s. What is the linear velocity of the javelin at release?
5. When throwing a discus, a track athlete has a final angular velocity (wf) of -5.5 radians/s. The radius of rotation was 1.3 m and the discus was accelerated for 1.2 seconds at an angular acceleration (a) of -5.9 radians/s2. Find wi, vi, vf, aT, & aCf.
6. A gymnast swinging on the uneven bars with a radius of rotation of 1.2 m has an initial angular velocity (wi) of 1.9 radians/s. The gymnast accelerates (a) at 2.3 radians/s2 for 0.4 seconds. Calculate wf, vi, vf, aT, aCi, aCf.
7. In the epic battle between David and Goliath, we make the following assumptions: David's sling is 1.5 m in length. He accelerates it from rest at 12 radians/s2 for 4 seconds. Calculate the final angular velocity (wf), final linear velocity (vf), tangential acceleration (aT), and final centripetal acceleration (aCf).
8. When kicking a soccer ball, a player had the following hip and knee angles, measured at 0.1 second intervals. Calculate the angular velocities and accelerations at each possible frame.
Frame Time qHip qKnee 1 0.0 245 70 2 0.1 200 75 3 0.2 145 92 4 0.3 150 145 5 0.4 153 176 6 0.5 155 179 Ball Contact