# Centripetal Force on a Spinning Cup

Centripetal Force on a Spinning Cup  principles in circular motion by having a cup of water seemingly defy gravity. The demonstration is used to explain centripetal acceleration, and a central force. While this demonstration takes some practice, it is one of the most fun and rewarding demonstration we have.

## Equipment

1. Platform with String
• This is the platform on which the cup will sit while being spun in circles
• Over time, the knots in the string will slip, and the platform will no longer be level. This can be fixed by untying and releveling the platform. Since this is quite tedious, the TA or instructor should be informed as soon as the platform seems to be slipping so that it can be repaired without a time constraint.
2. Cup for water
• Any transparent cup will work, but a cheap plastic one is ideal because the cup will eventually be launched across the room on accident.
3. Water
• Be sure to locate a source of water before starting your presentations.
• If you think you might spill water, you can practice with the tennis ball in the cup instead of water.
4. A brave/ well practiced demonstrator
• This demo is scary at first, but with practice can become second nature.

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## Physics Behind The Demo

In simplest terms, the water cup is undergoing uniform circular motion.

Uniform circular motion can be described as the motion of an object in a circle at a constant speed. As an object moves in a circle, it is constantly changing its direction. At all instances, the object is moving tangent to the circle. Since the direction of the velocity vector is the same as the direction of the object's motion, the velocity vector is directed tangent to the circle as well.

An object moving in a circle is accelerating. Accelerating objects are objects that are changing their velocity; either the speed or the direction. An object undergoing uniform circular motion is moving with a constant speed. Nonetheless, it is accelerating due to its change in direction. The direction of the acceleration is inwards and the object feels a net force pointing towards the center of teh circle.

The net force is an inward or “centripetal force”. Without such an inward force, an object would continue in a straight line, never changing its direction. Yet, with the inward net force directed perpendicular to the velocity vector, the object is always changing its direction and undergoing an inward acceleration.

To relate to the demo, as the water spins around, the centripetal force pushes the cup inward to the center of the circle and the water does not have time to accelerate downward. This is similar to the force that keeps you in your seat when doing a loop on a roller coaster. The water wants to fly off from the circle, but the bucket gets in the way and keeps it in place. This is the same effect you feel when you go around a tight corner in the car and get squished against the door or the force that keeps you in your seat when doing a loop on a roller coaster.

Ultimately, the force that is accelerating the platform and water cup toward the center is the tension in the string. The tension required to maintain circular motion is described in the following equation:

$$\mathbf{F}_{tension}={{mv^2}\over{r}}$$

The Tension force "$\LARGE\mathbf{F}_{tension}$" is the centripetal force. This equation shows that you must increase the inward force if you increase the velocity, or decrease the radius.

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## Performing The Demo

Each tab contains a different method for presenting this demo as written by a former outreach student.

### Before Spinning the Cup

1. Check that you have enough room around you so that you will not hit anyone or anything with the platform.
2. Place the cup filled with water in the center of the board and check that the board is level.
3. Begin by slowly swinging the platform back and forth to get a feel for it.
4. When you are comfortable, swing the platform quickly enough to get it going around in the circle.
5. When changing the orientation of the swing or the speed, do so slowly and deliberately. The more changes in acceleration there are, the more likely it is that the water will spill.
6. When you are ready to stop, do so when the platform is on the bottom of its swing.
7. Take a step in the same direction the platform is moving to give it a long enough time to slow down.

### Explaining the Demo

Sample "script"

“Alright so what I have here is a water cup that I’m going to spin around in a circle above my head. What do you guys think is going to happen?”

(Answers)

“Alright so let’s see if you guys are right.”

(Demonstrator proceeds to spin the water cup until it is over his head, or on his/her side if they aren’t comfortable with going overhead)

(As cup is spinning) “As you guys can see the water isn’t coming out. Can anyone tell me why?”

(Answers)

“Alright all good Ideas (stops spinning) Alright well the reason the water stays in the cup is what’s called centripetal force. All of you guys have experienced that same force in some way.”

(Awes of disbelief)

“So how many of you guys have ridden a roller-coaster that goes upside down?”

(Hands raise)

“Alright, have you guys ever wondered why you haven’t fallen out while you’re upside down? (Silence momentarily) Like I said it’s due to the centripetal force of roller-coaster. “

“Now all of you guys haven’t ridden roller-coasters, but all have you have ridden in cars right?” (Yeses)

“Alright, how many of your parents have made a really fast turn and you felt yourself being pulled to the side of the car? (All think)”

“That’s the same thing, centripetal force. While the car is changing direction you want to keep going straight so you hit the door. “

“How many of you guys liked this demonstration? Alright that’s what I like to hear. Next we have……”

## Tips

• Wrap the string around your finger a couple of times to make sure you have a good grip on it.
• Practice with a tennis ball in the cup before doing it with water.
• Don't be afraid of the demo, the worst that can happen is something gets wet. Kids are messy, everything in a school has been wet at some point.

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