Section 6.1, 6.2

1. Explain why centripetal force never shows up on a free body diagram.

2. Solve conical pendulum problems (horizontal circle).

3. Solve road bank problem given static friction = 0 (horizontal circle, see drawing at right).

4. Derive an expression for the critical speed of a roller coaster loop (vertical circle).

5. Derive an expression for the ramp height needed to achieve the critical velocity in a roller coaster loop (vertical circle).

6. Derive an expression for the tension in the rope used for swinging a mass at constant velocity in a vertical loop (vertical circle).

Homefun: Problems 13, 15, 21, 57, 55. Serway

Metacognition Problem Solving Principle 6.1: When solving a circular motion problem always ask which forces have components in the radial direction. The sum of these components is the centripetal force.

Metacognition Problem Solving Principle 6.2: All circles in the AP test will be either vertical or horizontal except for space stations in which case it doesn't matter. This is important since it indicates the plane which contains the radial direction (see Metacognition Principle 6.1)

Lesson 1

Key Concept: Centripetal force is the sum of the forces directed toward the center of rotation.

Purpose: Gain a deeper understanding of the circular motion equations.

Interactive Discussion: Objective 1. Why does centripetal force never appear on a FBD? 

Demo 1: Demonstrate the critical velocity in a vertical loop using a commercial loop track.

In Class Problem Solving: Objectives.

1. The conical swing.
2. Batman drives the Batmobile on a slippery slope.
3. The world's most exciting rollercoaster.
4. Loop the loop ramp height calculation.
5. Tarzan's amusement ride.

Resources/Materials: The loop the loop demonstration.

Section 6.3

7. Explain how fictitious forces appear both in systems which are accelerating in linear and uniform circular motion.

8. Find the angle a rope makes when it is suspended from the roof of an acceleration rail car.

Metacognition Problem Solving Principle 6.3: The sum of the components in the dimension  of acceleration provide the force causing linear acceleration.

Homefun: prob. 23, 25 Serway

Lesson 2

Key Concept: Fictitious forces

Interactive Discussion: Objective. Which of Newton's laws established where the frame of reference must be located?

In Class Problem Solving:

1. Rail car problem

Mini-Lab Physics Investigation (Requires only Purpose, data, and conclusion)

1. Measure height from the top of the circle.
2. Run multiple trials for both the steel roller and the mouse roller (rubber surfaced)

1. Why is the required height much greater than expected? Is it a problem with the mathematical model or just some form of random error or experimenter ineptitude? (Hint: If more energy was used than expected, it had to go somewhere. Click the button at the top labeled rotation and look for a possibility.)
2. Do both rollers have to start from the same height? If not, then why would one roller need to be started from a greater height than the other?