ScientistGrades 11–12⏱ 20 min

Circular motion

Swing a ball on a string, watch velocity and acceleration arrows, and cut the string to see where it goes.

Standards: HS-PS2-1

1Wonder

A car takes a curve at a steady 50 km/h. Its speedometer never changes, yet physicists say the car is accelerating. And when you swing a ball on a string and let go, which way does it fly?

2Explore

Swing it around

This activity needs a bigger screen

Turn your phone sideways, or open this lesson on a tablet or computer. The explanation and quiz below work here.

Radius r 1.5 m Speed v 4 m/s Mass m 0.5 kg

Try this

Watch the two arrows. Which one points along the circle? Which one points to the center?
Double the speed. How much bigger does the acceleration get?
Make the radius smaller at the same speed. Is it easier or harder to hold the string?
Press Cut the string. Does the ball fly straight outward, or along the dashed line?

3Explain

Step 1 of 5

Turning is accelerating

Going around at a steady speed, the velocity arrow keeps the same length but keeps changing direction. A change in velocity, even only in direction, is an acceleration.

Circular motion

\begin{aligned} a &= \frac{v^2}{r} \\ F &= \frac{m v^2}{r} \\ T &= \frac{2\pi r}{v} \end{aligned}

At a steady speed on a circle, the acceleration points to the center. A real force, such as tension, friction or gravity, must supply it.

4Practice

Question 1 of 5

A ball moves in a circle at a constant speed. Is it accelerating?

5Recap

Moving in a circle at steady speed is accelerating, because the direction changes.
The acceleration points to the center: a = v² / r.
It needs an inward force F = m v² / r (tension, friction, gravity…).
Without that force, the object moves on in a straight line along the tangent.