# PHYS 2211 Module 10.3

## Relating Angular and Translational Quantities 10.3 Relating Angular and Translational Quantities

### Learning Objectives

By the end of this section, you will be able to:

• Given the linear kinematic equation, write the corresponding rotational kinematic equation
• Calculate the linear distances, velocities, and accelerations of points on a rotating system given the angular velocities and accelerations Practice!

While the merry-go-round rotates with a constant angular velocity, the brother has the greatest centripetal (radial) acceleration. The centripetal (radial) acceleration is calculated with  where  is the angular velocity and r is the radial distance from the center of the circular path, in this case the center of the merry-go-round. Since the brother is farther from the center than the sister and they have the same angular velocity, the brother’s centripetal acceleration is greater.

They cannot have the same centripetal acceleration because they are different distances from the center of the merry-go-round. They cannot have zero centripetal acceleration because their velocity vectors are changing direction throughout the motion and a change in the direction of a velocity vector results in a centripetal acceleration.

While the merry-go-round rotates with an increasing angular velocity, the brother has the greatest tangential acceleration. Tangential acceleration is determined from the product of the angular acceleration and the radial distance from the center of the circular path: . Since the merry-go-round is increasing in angular velocity it has an angular acceleration, and this angular acceleration will be the same for the brother and the sister. Therefore, the brother, being farther away from the center of the merry-go-round, will have a greater tangential acceleration.

They cannot have the same tangential acceleration because they are different distances from the center of the merry-go-round. They cannot have zero tangential acceleration because they are increasing in angular velocity, which results in a tangential acceleration.