# PHYS 2211 Module 4.4

## Uniform Circular Motion 4.4 Uniform Circular Motion

### Learning Objectives

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

• Solve for the centripetal acceleration of an object moving on a circular path.
• Use the equations of circular motion to find the position, velocity, and acceleration of a particle executing circular motion.
• Explain the differences between centripetal acceleration and tangential acceleration resulting from nonuniform circular motion.
• Evaluate centripetal and tangential acceleration in nonuniform circular motion, and find the total acceleration vector.

### Centripetal Acceleration

In two- and three-dimensional kinematics, even if the speed is a constant, a particle can have acceleration if it moves along a curved trajectory such as a circle. In this case the velocity vector is changing, or .

A particle moving in a circle at a constant speed has an acceleration with magnitude

This is a radial acceleration and is called the centripetal acceleration, which is why we give it the subscript c. The word centripetal comes from the Latin words centrum (meaning “center”) and petere (meaning “to seek”), and thus takes the meaning “center seeking.” Practice! Discuss!

Consider how you would answer these questions. Then bring this to class for a group discussion.

A satellite has a circular orbit with an altitude of 640 km above Earth’s surface. Its period (the time for a particle to go around a closed path once) is 98.0 min. What is the satellite’s speed and radial acceleration?

A wheel 0.40 m in radius rotates at a constant rate of 180 rev/min. Find the speed and acceleration of a small stone lodged in the tread of the tire (on its outer edge).

A jet plane comes in for a downward dive as shown in the figure. The bottom part of the path is a quarter circle with a radius of curvature of 280 m. According to medical tests, pilots will lose consciousness when they pull out of a dive at an upward acceleration greater than 5.5g. At what speed (in m/s and mph) will the pilot black out during this dive?