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# How to Determine Centripetal Acceleration Which Keeps Things Moving in a Circle?

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Source:
Author: Jerry Silver

### The Idea

Pressing down with your foot on the accelerator of a car does not necessarily cause you to accelerate. You may be moving forward with constant velocity. How can you tell if you are accelerating? This experiment shows you a few ways to determine whether you are accelerating or just moving along at constant velocity.

In this project, you can also find ways to detect centripetal acceleration, which keeps things moving in a circle.

### What You Need

Any or all of the following "accelerometers" can be used to detect acceleration:

• pendulum: any weight on a string
• float tied to a string held underwater
• candle
• partially filled tank of liquid
• accelerometer, such as shown in Figure 5-1

### Pendulum

1. Holding the string of the pendulum, move at as steady a pace as you can. Observe the pendulum during constant velocity.
2. Now do the same thing, but observe what happens when you speed up (accelerate).

### Skateboard accelerometer

1. Attach a pendulum to a skateboard, as shown in Figure 5-2.
2. Roll it down a ramp that has a large enough slope for the skateboard to increase its speed. Observe the angle the pendulum makes with the vertical position.
3. Adjust the slope of the ramp, so the skateboard is just held on the ramp by friction without sliding down. This is called the angle of repose.
4. Give the skateboard a slight nudge. It should move at a fairly constant velocity. Note the angle of the pendulum.
5. What happens if the skateboard slows or goes up a ramp?

### Centripetal acceleration

Spin an apparatus, such as shown in Figure 5-3 or 5-4. A pair of candles at either end of a spinning board is another way to do this. The floating bob apparatus is commercially available or can be assembled from fishing bobs (or Styrofoam balls), baby food jars, a piece of wood with a hole in the center, and a metal post.

### Expected Results

A pendulum hangs vertically when moving at constant velocity. But it moves in the opposite direction as the acceleration it is experiencing. If an object slows down or decelerates, it shows up as a backward movement in the pendulum.

When the apparatus with the floating bob is spinning, the bob moves inward. This may be the opposite of what you might expect and is the opposite of what would happen with a freely hanging pendulum. The reason for this is the centripetal acceleration increases the buoyant force on the bob, forcing it inward. Candles move in the opposite direction. The flame moves outward, as does liquid in a container.

### Why It Works

Newton's second law requires that force and acceleration are related to each other through F = ma. If there is acceleration (a), there is a force (F) on the moving object (or mass, m). The force is in the same direction as the acceleration.

### Other Things to Try

An accelerometer, such as shown in Figure 5-4, directly indicates acceleration with a set of LEDs that light in proportion to the amount of acceleration. The greater the acceleration, the more LEDs will light. It can, for instance, indicate the acceleration of a cart pulled by a string. It can also be used to monitor centripetal acceleration.

### The Point

A hanging (or other unconstrained) object is affected by acceleration, but is not affected by uniform steady velocity.