### Unit 5: Circular Motion and Gravity

In this unit, we will study the simplest form of curved motion: uniform circular motion, or motion in a circular path at constant speed. In some ways, this unit is a continuation of the previous unit on dynamics, but we will introduce new concepts such as angular velocity and acceleration, centripetal force, and the force of gravity.

**Completing this unit should take you approximately 15 hours.**

Upon successful completion of this unit, the student will be able to:

- compare and contrast the physical properties associated with linear motion and rotational motion;
- explain why an object moving at a constant speed in a circle is accelerating;
- apply Newton's law of gravity;
- solve problems involving planets and satellites; and
- explain what it means when an astronaut in earth orbit is described as being "weightless".

### 5.1: Angular Velocity and Acceleration

Watch this lecture series, pausing to take notes, before moving on to the reading below.

This resource illustrates the connection between uniform circular motion and the simple harmonic motion associated with Hooke's Law.

Read sections 6.1 and 6.2 of "Chapter 6: Uniform Circular Motion and Gravitation". Look over the conceptual questions in each section to test your understanding.

Try solving these practice problems.

Study the animation, which illustrates the rule for determining the direction of the angular velocity vector.

Work on solving problems 1 through 6 in SAC116 and 1 through 6 in SAC117. The solutions are available, but make a serious attempt to solve the problems before looking at the solutions.

### 5.2: Centripetal Force

Watch this lecture series, pausing to take notes, before moving on to the reading below.

Read sections 6.3 and 6.4 of "Chapter 6: Uniform Circular Motion and Gravitation". Look over the conceptual questions in each section to test your understanding.

Try solving these practice problems.

The mass is constrained to move in a vertical circle while feeling the effects of Earth's gravity. Determine how the tension on the string must vary to make this happen as shown.

Work on solving problems 1, 2, and 3 from SAC119. The solutions are available, but make a serious attempt to solve the problems before looking at the solutions.

### 5.3: Newton's Law of Gravity

Watch this lecture series, pausing to take notes, before moving on to the reading below.

Read sections 6.5 and 6.6 of "Chapter 6: Uniform Circular Motion and Gravitation". Look over the conceptual questions in each section to test your understanding.

Try solving these practice problems.

Work on solving problems 1 through 4 from SAC115. The solutions are available, but make a serious attempt to solve the problems before looking at the solutions.

### Unit 5 Assessment

Take this assessment to see how well you understood this unit.

- This assessment
**does not count towards your grade**. It is just for practice! - You will see the correct answers when you submit your answers. Use this to help you study for the final exam!
- You can take this assessment as many times as you want, whenever you want.

- This assessment