# Activity Guide: Centripetal Acceleration

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Trick riders may just ride in circles, but that doesn’t mean they aren’t accelerating. Moving in a circle requires steady changes in direction. This is a form of acceleration directed inward, with a magnitude that depends on the velocity of the horse and rider and the radius of the circle. This is the same acceleration that we feel when going around bends in a car, and that holds us in our seat on the rollercoaster. This unit uses trick riding to show students the basics of circular motion.

## How to Incorporate the Video Into Instruction

This video can be used to motivate the study of centripetal acceleration and circular motion. It can also serve as an extra illustration to reinforce previous lessons on these topics. If you watch the video in class, ask students to pause the video while the horse runs around the ring. Ask them to describe how the components of the horse’s velocity are changing.

### Questions to Ask Students Before Watching the Video

1. What force does the horse exert?
2. What forces are acting on the horse?
3. How does the size the ring affect the speed at which the horse can gallop?
4. What kinds of acceleration do you see?

## Watch the Video

### Demonstration Opportunity

There are many ways to show centripetal acceleration in action. You can spin a penny on the bent end of a coat hanger, or spin a bucket full of water over your head. What’s the point? There has to be some sort of acceleration that counters gravity, so what is it? Where does it come from? Ultimately, it’s the tension in your arm holding the bucket or coat hanger. This is always directed toward the center of the circle, the object wants to go in a straight line, but it can’t because it’s being continually pulled off course.

1. Why does circular motion fit the definition of acceleration?
Because velocity is a vector, it has both direction and magnitude. Change either and you have acceleration. Changing direction is the same as changing the magnitude of components.
2. How does centripetal acceleration feel in real life?
It feels like a force pushing you into the car door when turning. It’s what keeps you in your seat on the rollercoaster, or plastered against the wall in the gravitron.
3. Why do you lean when riding in a car going around a bend?
The car pulls you along the turn, but your momentum wants to keep going in a straight line. This feels like a force pushing you away from the turn, but is really just your body resisting acceleration in accordance with Newton’s laws.
4. What happens for smaller radii and/or larger velocities?
Centripetal acceleration can be increased if the radius is decreased or velocity increased.

### Connections to Everyday Life

Most students will be familiar with centripetal acceleration from driving—going around turns. The faster you take a turn, the more you lean. Taking a tighter turn has the same effect. There are also numerous examples from the amusement park, rollercoaster, gravitron, etc.

One less obvious one might be the spin cycle on a washing machine. The water, unconstrained, goes flying off in straight lines. If you could accelerate in your car fast enough, for long enough, you could spin-dry your laundry in your trunk. Indy-style car racing is another one—why do cars change tires so much? The constant turning wears down rubber.

## Suggested Classroom Activities

### Activity 1: Rollercoaster Tycoon

The computer game “Rollercoaster Tycoon” has a data analysis section that allows players to find a number of physical quantities associated with the virtual rollercoaster’s they design. Have students design a rollercoaster, then calculate the various g’s of the vertical and horizontal loops using the velocity and radius measurements given by the program. Students can compare the values they calculate with those that the program automatically generates. Since the program takes into account things like friction, the values are likely to be slightly different, which makes for a good class discussion.

### Activity 2: Washers and Cork

Students can get a better sense of centripetal force by measuring the tension created by spinning a cork on a string. Tie a weighty cork or rubber stopper to the end of a strong string, or a bit of thin nylon rope. Thread the string or rope through a hand-width length of half-inch PCV pipe. Attach a hook at the other end suitable for hanging on the washers.

As the cork spins, it will pull up whatever weight is on the other end. This weight will be equal to the centripetal force keeping the cork moving in a circular motion. Students can verify this by measuring how fast the cork is spinning using a stopwatch. Multiplying π (pi) times diameter, then dividing by the time it takes for one rotation will give the magnitude of the cork’s speed. Students can then use this and the radius to find the centripetal acceleration.

### Activity 3: Centripetal Acceleration Video Analysis

To do this activity you will need to download the video "Video Analysis: Centripetal Acceleration (QT)". Use VideoPoint or similar software for graphing and analysis.

There are several clips of the rider going around the arena but the one that shows the overview of the horse is the best to use. A screen capture of the scene is shown below.

Have students mark the center of the arena as the origin. Have them use the 40-foot diameter as a scale for measurements. The purpose of this activity is to try to calculate the centripetal acceleration of the horse. To do this you need to have the velocity of the horse. An easy way to do this is to simply time the horse as it goes around the whole circle and use the circumference for the distance it traveled. Another way is to use the above VideoPoint graph to calculate the x and y velocities from the slope of the line. Use the Pythagoras Theorem to get the total velocity and simply plug into the centripetal acceleration formula.