### Unit 4: Dynamics

The study of motion is kinematics, which describes the way objects move, their velocity, and their acceleration. Dynamics consider the forces that affect the motion of moving objects. Newton's laws of motion are the foundation of dynamics. These laws provide examples of the breadth and simplicity of principles under which nature functions. They are also universal laws in that they apply to similar situations on Earth as well as in space.

**Completing this unit should take you approximately 26 hours.**

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

- compare and contrast mass and inertia;
- determine the net force on an object;
- draw and interpret free-body diagrams representing the forces on an object;
- identify the correct use of normal and tension forces in terms of Newton's third law of motion;
- use Newton's second law of motion to analyze dynamic problems;
- give examples of the effects of friction on the motion of an object;
- state Hooke's law;
- solve problems involving springs; and
- identify the fundamental physical properties of a simple pendulum, and describe the relationships among them.

### 4.1: Newton's First and Second Laws of Motion

Please click on the link above and watch this lecture series, pausing to take notes, before moving on to the reading below.

Read sections 4.1, 4.2, and 4.3 of "Chapter 4: Dynamics: Force and Newton's Laws of Motion". Look over the conceptual questions in each section to test your understanding.

Try solving these practice problems.

### 4.2: Newton's Third Law of Motion and Normal and Tension Forces

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

Read sections 4.4 and 4.5 of "Chapter 4: Dynamics: Force and Newton's Laws of Motion". Look over the conceptual questions in each section to test your understanding.

Try these practice problems, and be sure to make a serious attempt before viewing the answers.

Work on solving problems 1 through 4 from SAC112, problems 1 through 4 from SAC112A, and problems 1 through 3 from SAC113. The solutions are available, but make a serious attempt to solve the problems before looking at the solutions.

### 4.3: Applications of Newton's Laws of Motion

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

Read sections 4.6 and 4.7 of "Chapter 4: Dynamics: Force and Newton's Laws of Motion". Look over the conceptual questions in each section to test your understanding.

Try solving these practice problems.

Work on solving problems 1 through 10 from SAC114. The solutions are available, but make a serious attempt to solve the problems before looking at the solutions.

### 4.4: Friction

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

Read section 5.1 of "Chapter 5: Further Applications of Newton's Laws: Friction, Drag, and Elasticity". Look over the conceptual questions in each section to test your understanding.

Try solving these practice problems.

Work on solving problem 3 from SAC102. The solution is available, but make a serious attempt to solve the problem before looking at the solution.

### 4.5: Springs

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

Read section 16.1 on Hooke's Law and motion and energy associated with a spring. Look over the conceptual questions in the section to test your understanding.

Try solving these practice problems.

Examine this demonstration. Note that the spring always exerts force in the direction that returns the spring to its original unstretched length.

Work on solving problems 1 and 2 from SAC102 and 1, 2, and 3 from SAC109. The solutions are available, but make a serious attempt to solve the problems before looking at the solutions.

### 4.6: The Simple Pendulum

Read section 16.4 on the simple pendulum. Look over the conceptual questions in the section to test your understanding.

Try solving these practice problems.

Develop equations of motion for this pendulum that give predictions that agree with the simulated behavior. Is the tension on the string correct for a gravitational field of 9.8 m/s

^{2}?Work on solving problems 1 through 4 from SAC127. The solutions are available, but make a serious attempt to solve the problems before looking at the solutions.

### Unit 4 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