6.1 Rotation Angle and Angular Velocity
Arc length and radian measure, angular velocity as the rate a radius sweeps, and its link to speed at a spinning wheel's rim.
5 exercises
6.1 Exercise 2
Semi-trailer trucks have an odometer on one hub of a trailer wheel. The hub is weighted so that it does not rotate, but it contains gears to count the number of wheel revolutions—it then calculates the distance traveled. If the wheel has a 1.15 m diameter and goes through 200,000 rotations, how many kilometers should the odometer read?
6.1 Exercise 4
An automobile with 0.260 m radius tires travels 80,000 km before wearing them out. How many revolutions do the tires make, neglecting any backing up and any change in radius due to wear?
6.1 Exercise 6
A baseball pitcher brings his arm forward during a pitch, rotating the forearm about the elbow. If the velocity of the ball in the pitcher’s hand is 35.0 m/s and the ball is 0.300 m from the elbow joint, what is the angular velocity of the forearm?
6.1 Exercise 8
A truck with 0.420-m-radius tires travels at 32.0 m/s. What is the angular velocity of the rotating tires in radians per second? What is this in rev/min?
Integrated Concepts
When kicking a football, the kicker rotates his leg about the hip joint.
(a) If the velocity of the tip of the kicker’s shoe is 35.0 m/s and the hip joint is 1.05 m from the tip of the shoe, what is the shoe tip’s angular velocity?
(b) The shoe is in contact with the initially stationary 0.500 kg football for 20.0 ms. What average force is exerted on the football to give it a velocity of 20.0 m/s…
Adapted from College Physics © 2022 Rice University. Licensed under CC BY 4.0. Sources: College Physics 2e, College Physics for AP® Courses 2e. Imported at revision f98d7a7.