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UExcel Physics: Study Guide & Test Prep18 chapters | 201 lessons | 13 flashcard sets

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Lesson Transcript

Instructor:
*David Wood*

David has taught Honors Physics, AP Physics, IB Physics and general science courses. He has a Masters in Education, and a Bachelors in Physics.

After watching this video, you should be able to explain what centripetal force is, identify the centripetal force in a particular situation, and solve problems using the centripetal force equation. A short quiz will follow.

How many examples can you think of where an object moves in a circle? A car can drive in a circle. A lasso can be whirled around your head in a circle. And even planets orbit each other in circles. But what is it that keeps them moving in that circle?

What would you have to do to make the car move in a circle? You would have to push it - you would have to apply a force. A **centripetal force** is a force directed towards the center of a circle that keeps an object moving in a circle.

But hold on a minute. Imagine you're in a car, and that car takes a sharp right turn. What force do you feel? Which way are you pushed? It feels like you're pushed, not inwards, but outwards - towards the outside of the circle. Or if you've ever been on a fairground ride that spins and holds you against the outside wall, it's the same effect. This feeling of being pushed out is called the **centriFUgal force**, or cenTRIFugal force, a force pointing away from the center of a circle.

But the centrifugal force you feel is a fictitious force - it isn't real. The only force that applies to you is the centripetal one that keeps you in the circle. So why do you feel like you're being pushed out?

Well, when you sit in a car moving in a straight line, your body, like any object, wants to keep moving in a straight line. Newton's First Law says that a body in motion stays in motion, a body at rest stays at rest, unless acted upon by an unbalanced force. The car tries to turn the corner, but your body wants to keep going straight, so you get pushed towards the outside of the car as your body tries to continue in a straight line. If it wasn't for the centripetal force provided by the friction between you and the car seat and the seat belt, and the normal force the side of the car applies to you, you would indeed just... keep going.

The centripetal force is nothing mysterious, but it sounds kind of like it is. People will often make the terrible mistake of drawing Fc for centripetal force on a free-body force diagram. Never, ever do this. The centripetal force in a given situation is always created by a specific, real-life force. A satellite is kept in orbit by gravity - gravity, Fg, is the centripetal force. A ball whirled on a string over your head is held in place by tension, FT. And the car moves in a circle because of friction, Ff. There is always a specific force that plays the role of the centripetal force - you just have to figure out what it is!

The equation for centripetal force says that the centripetal force, Fc, measured in newtons, is equal to the mass of the object moving in a circle, m, measured in kilograms, multiplied by the velocity of the object as it goes around the circle, v, measured in meters per second, squared (it's just the velocity that's squared), divided by the radius of the circle, measured in meters.

Fc = mv^2 / r

So for example, if gravity is the centripetal force, because we're looking at a satellite in orbit, then you could say that the force of gravity (given by the equation F = mg or Fg) is equal to mv-squared over r.

Fg = mv^2 / r

Okay, let's go through an example of how to use the equation.

Imagine you're spinning that lasso, but this time you attach a mass to the end of it. If the spinning lasso is 2 meters long, and the mass of the... mass, is 0.1 kilograms, and the mass is moving around the circular path at a speed of 3 m/s, what is the force of tension in the lasso?

The first step, as always, is to write down what we know. We have the length of the string, which in this case is the radius of the circle, so r equals 2 meters (r = 2 meters). And we have the mass of 0.1 kilograms (m = 0.1 kilograms). And we have the velocity of 3 m/s (v = 3 m/s). And we want the force of tension, FT.

Since the mass is moving in a circle, the force of tension is acting as our centripetal force.

Fc = mv^2 / r, which means for this situation, FT = mv^2 / r.

.1 (3) ^2 / 2 = 0.45 newtons

And that's it; we're done.

A **centripetal force** is a force directed towards the center of a circle that keeps an object moving in a circle. When you're actually moving in a circle; however, you get a feeling of being pushed outwards, which is called the centriFUgal force, or **cenTRIFugal force**, a force pointing away from the center of a circle.

This is because your body, like any object, wants to keep moving in a straight line as explained by Newton's First Law. But if it wasn't for the centripetal force provided by the friction between you and the car seat and seat belt, and the normal force between you and the side of the car, you would just keep going in that straight line. So the force that you actually feel is pointed towards the center of the circle - a centripetal force.

A common mistake is drawing Fc for centripetal force on a free-body force diagram. But the centripetal force in a given situation is always created by a specific, real-life force, whether gravity, tension in a string, or the normal force.

The equation for centripetal force says that the centripetal force, Fc, measured in newtons, is equal to the mass of the object moving in a circle, m, measured in kilograms, multiplied by the velocity of the object as it goes around the circle, v, measured in meters per second, squared (it's just the velocity that's squared), divided by the radius of the circle, measured in meters (Fc = mv^2 / r).

Following this lesson, you should be able to:

- Define centripetal force and centrifugal force
- Explain how Newton's First Law applies to these forces
- Recall how to correctly draw a free-body diagram when working with problems involving centripetal force
- Identify the equation for centripetal force

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UExcel Physics: Study Guide & Test Prep18 chapters | 201 lessons | 13 flashcard sets

- Go to Vectors

- Go to Kinematics

- Newton's First Law of Motion: Examples of the Effect of Force on Motion 8:25
- Distinguishing Between Inertia and Mass 6:45
- Mass and Weight: Differences and Calculations 5:44
- State of Motion and Velocity 4:40
- Force: Definition and Types 7:02
- Forces: Balanced and Unbalanced 5:50
- Free-Body Diagrams 4:34
- Net Force: Definition and Calculations 6:16
- Newton's Second Law of Motion: The Relationship Between Force and Acceleration 8:04
- Determining the Acceleration of an Object 8:35
- Determining the Individual Forces Acting Upon an Object 5:41
- Air Resistance and Free Fall 8:27
- Newton's Third Law of Motion: Examples of the Relationship Between Two Forces 4:24
- Newton's Laws and Weight, Mass & Gravity 8:14
- Identifying Action and Reaction Force Pairs 8:12
- The Normal Force: Definition and Examples 6:21
- Friction: Definition and Types 4:15
- Inclined Planes in Physics: Definition, Facts, and Examples 6:56
- Hooke's Law & the Spring Constant: Definition & Equation 4:39
- Centripetal Force: Definition, Examples & Problems 5:57
- Go to Force and the Laws of Motion

- Go to Relativity

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