Becky McCoy

Lesson Title: Circular Motion Lesson 2 Timing: 60 minutes

Target Audience:11th and 12th grade Physics class

Objectives:Students Will Be Able To:

Describe circular motion using centripetal acceleration Describe circular motion using linear and angular acceleration

The Teacher Will Be Able To: Assess student understanding of centripetal acceleration Give students opportunities to observe centripetal acceleration and circular

motion

Standards Assessed: New York State Standards Standard 4.5.1 Explain and predict different patterns of motion of objects (e.g.,

linear and uniform circular motion, velocity and acceleration, momentum and inertia).

o xi. Verify Newton’s Second Law of Circular Motion

Misconception(s) Addressed: Centrifugal force Differences between linear and angular velocity Relationship between circular motion, velocity, time, and radius

Prior Knowledge: Mechanics and Kinematics units, Circular Motion Introduction

Aim: Demonstrate instances of Centripetal Acceleration and describe using linear and angular velocity.

Concept Map Vocabulary:No Concept Map for this unit.

Necessary Preparation:

COPIES

MATERIALS Rubber washer, string, straw Large beaker with rubber ball Flask beaker, popcorn foam, string, rubber stopper Cup on a string Water

Becky McCoy

SET UP Assemble rubber washer, string, straw (from last class) Assemble one Accelerometer (tie string around foam, fill beaker with water, put

foam/string in beaker so when the beaker is sealed and turned upside down, the foam floats near the top of the beaker)

Becky McCoy

Lesson Plan

Aim: Demonstrate instances of Centripetal Acceleration and describe using linear and angular velocity.

Physics Push-Up: Think-Pair-ShareHave students talk with a partner about what we discussed yesterday. Listen for key words such as: centripetal acceleration, velocity, and Newton’s First Law.

Activity: Centripetal Acceleration and Angular Velocity ProofsMaterials:

Rubber washer, string, straw Large beaker with rubber ball Flask beaker, popcorn foam, string, rubber stopper Water

Procedure: Review the definition of Centripetal Acceleration and Force. Ask some basic

questions from last class (“If a car is turning left, what will you feel? What keeps you from continuing straight?”)

Do a Banked Track Race Car drawing on the board (see diagram on the right).

Assume the car weights 700kg and the track is banked at 10degrees (this could also simulate a normal car turning on an average road, so you don’t have to use the race car example). Calculate the normal force (6860N).

Point out that there is a horizontal component that is not accounted for (friction can be neglected because it opposes the motion, which means it is coming in/out of the page).

Alter the drawing to show this “mystery force”. Define this force as the Centripetal Force. Given

even a slight bank, a center-seeking force is present.

FUN FACT: when racing, the faster your velocity, the higher up you are on the banked curve.

Have students create their own accelerometers and let each student have an opportunity to spin around and observe the acceleration pointing into the circle (towards you at all times).

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PROOF #2: Draw a large circle on the board. Using three different colors, label three radius and three velocities, like the diagram below (label the and the right angle).

Ask to be sure all students agree that the radius and velocity are perpendicular to each other.

Draw two of the velocities with their tails together (second diagram). The resulting vector is in the direction of the center of the circle! This can easily lead to a proof of centripetal acceleration: a = v2/r

o This triangle (when drawn well) will be a similar triangle to those in the circle. This means we can create a ratio. The arc(ab) can be written as the velocity multiplied by the change in time – the circle image. Therefore, the first part of the ratio can be written as v*t/r. The triangle diagram shows the change in velocity divided by the magnitude of the velocity is analogous to the first part.

o v*t/r ~ v/vo Now we want to get the deltas on the same side.o (v^2)/r ~ v/to And we know that v/t is also equal to acceleration. So…(v^2)/r ~ ao But, this is only an approximation, so we’ve got to figure out how to

make it exact. Well, as the angle between the vectors approaches zero (again referring to the circle diagram), the arc(ab) approaches a straight line. And as the change in time approaches zero (as measurements become more instantaneous), the velocity becomes perpendicular to the acceleration. This means the approximation we made can be exact – both the velocity and radius are perpendicular to the acceleration.

o (v^2)/r = a !!!o This linear velocity can be written as 2r/T.

Ask students to define linear velocity (the change in distance over a certain time).

Becky McCoy

Ask students to guess what angular velocity might be (the changing angle over a certain time).

Write out an equation for angular velocity: = /t. Get the string/rubber washer/straw combination and, holding the straw in one

hand and the string in the other, swing the washer in a horizontal circle over your head. Stop spinning and slowly pull the string down, showing that the washer’s linear velocity increases.

Ask students whether the linear velocity, angular velocity, or both change. Show the radius decreases and so does the time (or period), causing no net change

in the linear velocity. However, for the angular velocity, the angle stays the same and the time changes,

so the net angular velocity changes as well.

Activity Summary: Don’t Spill The Water!Fill the cup on a string with water and have students spin it vertically and horizontally without spilling. Have students describe what forces are acting on the water and why it doesn’t spill.

Homework:Mathematical problems TBD

Exit Strategy:321 Exit Cards – 3 examples of circular motion, 2 types of velocity used in circular motion, 1 type of acceleration in circular motion

Extension Activity:Practice several examples of centripetal acceleration and angular momentum.

Assessment:Exit cardsFormative assessment listening to student conversations, comments, and answers

Resources:

Notes & Adaptations: