Circular Motion

Circular motion is when an object moves around a circle. Even if its speed stays the same, its direction keeps changing. Changing direction means the velocity is changing, so the object is accelerating.

Why a force is needed

To keep moving in a circle, an object needs a force pulling it towards the centre. This inward force is called the centripetal force (centre-seeking). Without it, the object would move off in a straight line due to inertia.

You may feel as if you are pushed outward in a turning car. This is your body trying to keep going straight while the car turns inward. The real force on you is inward (from the seatbelt or friction with the seat).

What provides the inward force?

• Friction between tyres and road when a car turns.
• Tension in a string when you swing a ball.
• Gravity for planets and moons in orbit.
• Normal/contact force in loops or bends on a roller coaster.

How changing factors affect circular motion

• At the same mass and radius, increasing the inward force can allow a higher speed.
• At the same mass and speed, increasing the inward force makes the circle tighter (smaller radius).
• For the same speed and radius, a larger mass needs a larger inward force.

Speed in a circular path

One lap around a circle is the circumference, which is the distance $2\pi r$. If one lap takes time $T$ (the period), the average speed is:

$$v = \frac{2\pi r}{T}$$

Real-world connections

• Turning in a car: friction provides the inward force.
• Swinging a bucket of water in a vertical circle: the handle’s tension pulls inward.
• Earth orbiting the Sun: gravity pulls Earth toward the Sun.

Common misconceptions

• “There is an outward force.” In fact, the needed force is inward. The outward “feeling” is inertia.
• “No acceleration if speed is constant.” In circular motion, acceleration exists because direction changes.