## Subjects

# Uniform circular motion

True or false? Speed is the same thing as velocity.

## Uniform circular motion

Jenny got a new electric skateboard. She’s excited to try it out in this flat car park, so she hops on and starts rolling. The skateboard has an engine that keeps it at a constant speed. For as long as there is no other force acting on Jenny and her skateboard, she will continue going in the same direction and at the same speed. We know this from Newton’s first law of motion, which states that an object in motion will continue moving in a straight line at a constant speed unless acted on by an outside force.

But what’s this? Jenny’s trying something different… She takes a rope and attaches it to a lamppost in the middle of the car park. She holds the other end of the rope and moves away from the lamppost, so the rope is stretched. What will happen when she turns on the engine and starts moving? Let’s take a look from above!

She is going in a circle! Jenny is going at a constant speed along a circular path. She’s in what we call a uniform circular motion. The radius of her circular path is equal to the length of the rope between her and the lamppost. But why is she turning?

According to Newton's first law, she should be moving in a straight line… unless there is an outside force! When Jenny is on her skateboard, despite her trying to move forward, the rope is holding her. There is a force acting along the rope, from Jenny towards the lamppost in the centre. As Jenny moves around the circular path, the direction of the force keeps adjusting, so that it always points towards the centre of the circle. This force is the centripetal force.

Centripetal force is what causes Jenny’s circular motion. Let’s recap: uniform circular motion is a motion with a constant speed along a circular path, caused by centripetal force, which always points towards the centre of the circle. Now, let’s see what else we can observe. The distance Jenny travels every round equals the circumference of a circle — 2 π r. R is the radius of the circle — in this case the length of the rope.

It always takes her the same amount of time — her speed is constant. We can determine her speed by dividing the distance she travels by the time it takes her, T. We get this formula: speed equals 2 π r divided by T. This is a formula for speed in uniform circular motion. How about Jenny’s velocity?

Is it constant too? Velocity has both magnitude and direction. The magnitude of Jenny’s velocity is equal to her speed, and we can calculate it with the same formula — 2 π r divided by t. And what’s the velocity’s direction? Let’s take a look again.

At every point of her circular path, Jenny is facing forward. If she drops the rope, she continues moving in a straight line from there, as there is no more centripetal force acting on her. This is the direction of her velocity at the moment she drops the rope. Let’s do it again, and see what happens if she lets go of the rope in a different place. She goes straight ahead from that point too, in a different direction than before!

The direction of Jenny’s velocity is different, depending on her position along the circular path! In uniform circular motion, the direction of velocity is always perpendicular to the direction of the centripetal force. We say it’s tangent to the circular path, and we call it tangential velocity. Tangential velocity is not constant, because its direction changes all the time. But that’s enough physics for today!

Go on and show us some cool tricks, Jenny!