Constant speed, yet accelerating

The idea

Uniform circular motion is accelerated motion: the speed stays constant, but the direction of velocity changes continuously, and any change in velocity means a non-zero acceleration.

A steady speedometer

A scooter goes round a circular track. The speedometer needle stays at the same reading all the time.

Do you think the scooter has an acceleration?

• Yes, because its direction keeps changing
• No, because its speed is constant
• No, because it stays on the same track

Two points on the circle

Move point 2 round the circle. Compare the two velocity arrows.

Velocity is more than speed

The two red and blue arrows were equally long, so the speed was the same. But they pointed in different directions, so the velocity was different. A change in velocity means an acceleration, even when the speed does not change.

Uniform circular motion is accelerated motion: the speed stays constant, but the direction of the velocity changes continuously, and any change in velocity means a non-zero acceleration.

Notes

In uniform circular motion the speed is constant but the direction of velocity changes continuously: any change in velocity means non-zero acceleration.

Check yourself

An object moves in uniform circular motion. Is its motion accelerated?

Any change in velocity means…

In uniform circular motion, which of these stays the same?

A friend says acceleration needs a change in speed. What does uniform circular motion show?

• No, because its speed is constant. Velocity has a direction as well as a magnitude. When the direction changes, the velocity changes, so there is an acceleration.
• No, because it returns to the start. Returning to the start does not matter. The velocity changes at every instant, so there is an acceleration.
• Yes, because the direction of its velocity changes continuously — correct. Yes!
• a non-zero acceleration — correct. Yes!
• a zero acceleration. Acceleration is non-zero whenever the velocity changes.
• a change in the speed only. Velocity can change when only its direction changes, with the speed staying the same.
• The velocity. The direction of the velocity keeps changing, so the velocity does not stay the same.
• The speed — correct. Yes!
• The direction of the velocity. The direction of the velocity changes continuously.
• Acceleration needs a change in direction, not a change in speed. Acceleration comes from any change in velocity, so a change in the speed (the magnitude) also gives it.
• Nothing, the friend is right. In uniform circular motion the speed is constant, yet the motion is accelerated.
• Acceleration can happen with a constant speed, if the direction of the velocity changes — correct. Yes!