# Uniform Circular Motion & Gravity

Now that you’ve talked about linear and projectile kinematics, as well as fundamentals of dynamics and Newton’s Laws, you have the skills and background to analyze circular motion. Of course, this has obvious applications such as cars moving around a circular track, roller coasters moving in loops, and toy trains chugging around a circular track under the Christmas tree. Less obvious, however, is the application to turning objects. Any object that is turning can be thought of as moving through a portion of a circular path, even if it’s just a small portion of that path.

With this realization, analysis of circular motion will allow you to explore a car speeding around a corner on an icy road, a running back cutting upfield to avoid a blitzing linebacker, and the orbits of planetary bodies. The key to understanding all of these phenomena starts with the study of uniform circular motion.

### Objectives

- Explain the acceleration of an object moving in a circle at constant speed.
- Define centripetal force and recognize that it is not a special kind of force, but that it is provided by forces such as tension, gravity, and friction.
- Solve problems involving calculations of centripetal force.
- Determine the direction of a centripetal force and centripetal acceleration for an object moving in a circular path.
- Calculate the period, frequency, speed and distance traveled for objects moving in circles at constant speed.
- Analyze and solve problems involving objects moving in vertical circles.
- Determine the acceleration due to gravity near the surface of Earth.
- Utilize Newton’s Law of Universal Gravitation to determine the gravitational force of attraction between two objects.
- Explain the difference between mass and weight.
- Explain weightlessness for objects in orbit.
- Explain how Kepler’s Laws describe the orbits of planetary objects around the sun.

### Topics of Study

### Video Tutorials

- Centripetal Acceleration
- Circular Speed
- Centripetal Force
- Frequency and Period
- Vertical Circular Motion
- Universal Gravitation
- Gravitational Fields
- Orbits