Scene #

Description

Narration

1

Uniform Circular Motion is at the top of the slide. Arrows are drawn going in a circle. There is an orange dot at the top of the circle. The narrator draws a green arrow from the orange dot going to the right out of the circle and labels it v. From the orange dot he draws another arrow that is red going down into the circle and labels it F-sub-c.

Before we begin our study of centripetal force, let's begin by reminding ourselves how uniform circular motion occurs. During uniform circular motion, an object is moving in a circle at a constant speed. And its velocity vector at any given moment will be tangential to the circle, like that.

But we know from Newton's first law that a change in direction requires an outside force. And circular motion is a constant change of direction. So, there must be a constant force applied.

And that force is the centripetal force. Just like centripetal acceleration, it is an inward-pointing force that causes the constant change in direction that uniform circular motion requires.

Now, what supplies that outside force will vary from situation to situation. For a car driving in a circle, it's the friction of the tires that supplies the centripetal force. For an object spinning on a string, it's the tension in the string that supplies the centripetal force. For a moon orbiting a planet, it's the gravitational attraction that supplies that centripetal force.

The source of the centripetal force will vary from situation to situation. But it will always be pointed inward, just like centripetal acceleration.

2

The definition for Centripetal Force is on the screen, the narrator reads it out loud. A formula that represents the definition of Centripetal Force. He then writes an equation for centripetal acceleration. From that he writes in green another equation for Centripetal Force.

Now let's examine centripetal force. Centripetal force is often abbreviated F sub c. And it's the center-seeking force that causes centripetal acceleration. Like the centripetal acceleration vector, it always points inward.

Centripetal force is defined by a special case of Newton's second law. And that's F sub c equals m times a sub c. Centripetal force equals mass times centripetal acceleration.

We know from our previous study of centripetal acceleration that that can be defined as speed squared divided by radius. And if we substitute this definition for centripetal acceleration into our definition for centripetal force, then we get the following equation. Centripetal force equals mass times speed squared divided by radius.

And we can use either of these equations to calculate centripetal force in a given situation. You simply use whichever one is more appropriate for a given problem.

3

The narrator reads a problem out loud. For part a, the narrator writes down the information known to help answer the question in red. He says it out loud as he writes it. He then writes in blue the steps to solving the problem saying the steps out loud as he writes.

So, let's look at a centripetal force problem and see how we can use this information.

The problem reads, "for an airshow, a 79.5 kilogram stunt pilot is flying in tight circles above the crowd. The circles are of radius 122 meters, and it takes the pilot 9.95 seconds to complete a single circle."

The first part of the question asks, "what is the pilot's speed?" Well, let's begin by writing down what information we know. We know that the pilot's mass is 79.5 kilograms. We know that the radius of the circle the pilot is flying in is 122 meters. And we know that the period of rotation for the pilot is 9.95 seconds.

Speed is defined as distance over time. In this case, the distance covered in a single rotation is equal to 2 pi r, the circumference of the circle the pilot is flying in. And the time it takes to cover that distance is equal to the period, T.

Substituting in the values we know, we get 2 times pi times 122 meters divided by the period of 9.95 seconds. 2 times pi times 122 gives us 766.5 meters, a time of 9.95 seconds. Dividing that out gives us that the pilot's speed is 77.0 meters per second.

4

The narrator pulls up part b of the problem. In green he writes out the formula and steps for solving part b saying the steps out loud as he writes them.

Now let's look at the next part of the problem. The next part asks, "what is the pilot's centripetal acceleration?" Centripetal acceleration, as we discussed before, is defined by the equation speeds squared divided by radius.

We calculated the speed in the previous part of the problem. That's 77 meters per second-- so that quantity squared divided by the radius, which was given to us as 122 meters. Multiplying that out gives us 5,929 meters squared per second squared divided by 122 meters. Enter that into your calculator, and you'll find that the centripetal acceleration for the pilot is equal to 48.6 meters per second squared.

5

The narrator pulls up part c and writes in blue the steps to solving the problem. He says the steps out loud as he writes them.

Now let's look at the last part of the problem, which asks, "what is the centripetal force acting on the pilot?" Again, we define centripetal force to be the product of mass and centripetal acceleration.

We know mass to be 79.5 kilograms. And the centripetal acceleration we calculated to be 48.6 meters per second squared. Multiply those together, and you get that the centripetal force acting on the pilot is approximately 3,860 newtons.