1. Circular Motion Standards:
1f Students know applying a force to an object perpendicular to the direction of its motion causes the object to change its direction but not speed (e.g. Earth’s gravitational force causes a satellite in a circular orbit to change direction but not speed).
1g Students know circular motion requires he application of constant force directed toward the center of the circle.
1L Students know how to solve problems in circular motion by using the formula for centripetal acceleration in the following form a =v2/r.

2. Circular motion requires an inward force
Examples
Water in bucket -road on car
Ball on string car door on driver
Motorcycle in motordrome -Earth on moon
Inward forces for above are
Bucket on water -friction from road
Tension of string -normal force from door
Normal force from track -gravity
These forces are said to be in the centripetal direction and thus centripetal forces
Question: What are the forces that keep the following objects moving in a circle: a) water in bucket spun in vertical circle b) ball whirled around on string c) motorcycle in motordrome d) car rounding a flat curve e) passenger in car that is rounding a curve f) Earth on moon or satellite circling Earth.
Activities:
Bucket and water demo: Take bucket partially filled with water and make a vertical circle with it showing that no water is lost. Ask what is force that keeps water in bucket. Point out that water at bottom wants to go in straight line due to its inertia and that bucket gets in way and pushes it towards center of circle. Take hand to represent water and slap it inward indicating bucket force. Draw situation on board.
Demo: Ball on string. Whirl ball on string in horizontal circle. Point out that tension of string provides inward force. Draw freebody diagram of ball and string on board. Add gravity but point out that its direction cannot affect the circular motion in this case since it is in a different direction.
Video: Motorcycle and car in motordrome: Show video on DVD and draw free body diagram for car. Again point out that there is a force towards the center of the circle from the track this time. Friction up and weight down are equal in magnitude and do not affect the circular motion.
Car on level road Example: Draw car moving around normal turn and point out the inward force of the road on the tires which keeps the car from skidding into its inertial path. Discuss passenger inside car and how door provides inside force.
Earth on satellite example: Draw Earth with Moon orbiting it. Ask what force acts on Moon and point out that it is gravity. Point out that again this is an inward force relative to the circular motion. Draw a satellite and ask what are forces on it. Draw free body diagram.
Finish by stating that any circular motion requires a net inward force. We sometimes classify any inward force as a center seeking or centripetal force.

3. Check Questions
A ball is whirled around on a string as shown from above in the picture. If the string is cut at the position shown, what is the path of the ball? B D A E C
Show youtube video on hammer throw.

4. Inward force causes change in direction but not speed.
Examples
Water in bucket road on car
Ball on string car door on driver
Motorcycle in motordrome -Earth on moon
Centripetal or inward force in all of these examples is perpendicular to direction object is traveling at that moment.
These centripetal forces cannot do work on moving object and the speed will remain constant.
Inward or centripetal force changes direction of object but not speed.
Question: Does the inward force that results in circular motion change the direction of an object? Does it change the speed of the object? Does it do work on the object? Does it change the velocity of the object?
Activities:
Point out that in each example the force causing circular motion was perpendicular to the motion of the object. This means the force can do no work on the object and can only change the direction of the object. Speed is not changed by this force.
Remind students that velocity is a vector with magnitude and DIRECTION. Since the direction of the object is changed, velocity is changed by centripetal forces.

5. Check Question
A block of ice slides along a smooth surface. Will forces in the following directions affect the speed, direction or both of the block?
Force is in same direction of motion
Force is in opposite direction of motion
Force is perpendicular to direction of motion
Direction only is affected
Speed only
Speed and direction

6. The magnitude of the inward force depends on the mass, radius of curvature, and velocity
Centripetal force increases proportionally w/ mass made to move in circle
Centripetal force increases as the square of the tangential speed
Centripetal force decreases linearly w/ increase of radius of curvature
Fcentripetal = mass x tangential velocity2/ radius =mv2/r where v2/r is sometimes called the centripetal acceleration.
Just Newton’s 2nd law w/ a special acceleration
Questions: How is the magnitude of the inward force required to keep an object moving in a circle related to the object’s mass, speed and the radius of the circle’s curvature? Write a mathematical equation that summarizes these relationships. What is the v2/ r term sometimes called?
Activities:
Again spin ball in horizontal circle and ask if you will need more force, feel more force if the ball is spun faster or slower. Write on board that as v increases, F increases.
Ask if larger or smaller ball requires more centripetal force to keep moving in a circle. Write on board that as mass increases so does centripetal force needed.
Ask about spinning in a small or large circle. Point out that small circle involves turning more quickly. Draw two circles on board to demonstrate this. Write that as radius increases, centripetal force decreases.
Write out formula for centripetal force. Underline part which is called centripetal acceleration and state that this is just a fancy version of Newton’s second law especially for circular motion.

7. Check Question
A ball is whirled on the string in a horizontal circle. Which of the following changes will increase the centripetal force needed to keep the ball moving in a circle?
Increasing the speed the ball is whirled
Increasing the mass of the ball
Increasing the radius of the circle the ball is making
A and B only
All of these

8. Centrifugal Farce
Centrifugal force would be a center fleeing or outward force
Bug whirled around in can example
Thrown to outside
Bug will claim that force is acting on it but outside viewer knows bug is simply following inertial path
Centrifuge example
Separates materials according to its inertia/mass
Should be called an inertiafuge!
In above cases there is no interaction thus no outward force
Centrifugal force
Question: In what direction would a centrifugal force act relative to the center of the circle? Why is such a force often considered a false force? What usually is the cause of this “force?”
Activities:
State that in contrast to an inward centripetal force sometimes people use the word centrifugal or center-fleeing force to explain outward motion during a turn.
Example: Go through bug in can example. Ask if bug is thrown to outside or inside of can if spun around? Ask what causes this and convince class again that it is the bug’s inertia. Point out that bug would move in straight line path except for fact that the bottom of the can provides an inward force. State that bug still feels pulled outward and since it doesn’t know about circuar motion it assumes there is some “gravitational” force pulling her out. We from the outside realize thee is no outside body thus no outside force and it is only her inertia that is causing this.
Discuss centrifuge and how it is poorly named.
Discuss carnival ride where floor falls out from beneath you

9. Artificial Gravity on Space Station
Bug in spinning tire
Faster spin means thrown against wall harder
Larger tire means thrown against wall softer
In center of axle, bug will simply rotate and not be thrown at all
For rotating circular space station
Faster spin means you would gain “weight”
As move toward center you would lose “weight”, at center you’re weightless
1 km diameter station will reach 1 g when rotating once every 45 seconds , with tangential speed of 252 km/hr
2 km diameter station will reach 1 g when rotating once every 60 seconds, with tangential speed of 378 km/hr
Currently rotating at 1000 km/hr here on Earth
Gravitational acceleration = v x v /r,
period = (4 pi x pi x r / g) ½
R = g TxT / 4 pi x pi
V tan =2 pi r/ T

10. Odds and Ends Tangential vs rotational or angular speed
Tangential speed is a linear speed measured in meters/ second and the like
Angular speed is measured in radians/second
Tangential speed increases as move away from center, angular speed remains constant
Centripetal vs. angular acceleration
Centripetal acceleration is a linear acceleration measured in m/s/s and directed towards the middle of the circle (a=v2 /r)
Angular acceleration is measured in radians/sec/sec, and measures increase or decrease in spin rate