A 2 kg ball moves at 6 m/s in a circle of radius 3 m. What centripetal force is required?

The correct answer is: 24 N. F = mv²/r.

If you double the speed while keeping radius fixed, how does the centripetal force change?

The correct answer is: It quadruples. F ∝ v² — doubling speed quadruples force.

A car rounds a flat curve of radius 50 m at 20 m/s. What friction force is needed? (m = 1200 kg).

The correct answer is: 9,600 N. Friction provides centripetal force: f = mv²/r.

Pro 🔒~15 min

Circular Motion & Centripetal Force

Why objects curve instead of fly off

How it works

Uniform circular motion requires a net inward (centripetal) force to continuously change the direction of velocity. This force is NOT a new type of force — it is provided by tension, gravity, normal force, or friction depending on the situation. The centripetal acceleration always points toward the center, while velocity is always tangential. Remove the centripetal force and the object moves in a straight line (Newton's 1st Law).

Does a ball on a string get pulled outward when you spin it? Hint: there is no centrifugal force!

What you feel as 'centrifugal force' is actually your hand providing the inward pull — remove it, and the ball flies straight, not outward.

What you'll learn

Centripetal vs. Centrifugal. Centripetal means 'center-seeking.' The ball on a string is always being pulled inward by tension. 'Centrifugal force' is a fictitious force that only appears in a rotating reference frame — in an inertial frame, there is no outward force.
The v²/r Relationship. Centripetal acceleration equals v²/r. This means doubling the speed requires four times the inward force to maintain the same circular path. The acceleration always points toward the center, perpendicular to velocity.
Force = Mass × Centripetal Acceleration. The net inward force equals mv²/r. This is not a new type of force — it is provided by tension, gravity, friction, or normal force depending on the situation. Identifying what provides the centripetal force is the key skill in circular motion problems.
What Happens When the Force Disappears?. Cut the string and the ball flies off tangentially — not outward! This is Newton's first law in action: without a net force, the object continues in a straight line along its instantaneous velocity direction.

Step-by-step

Adjust radius and speed.
Watch how the centripetal force vector (arrow) changes magnitude and always points inward.
Increase speed while keeping radius fixed — feel how much more force is required.
Use the 'cut string' toggle (Pro) to see the ball fly off tangentially.

Key formulas

$a_c = \frac{v^2}{r}$ Centripetal acceleration
$F_c = \frac{mv^2}{r} = m\omega^2 r$ Centripetal force (directed inward)
$T = \frac{2\pi r}{v}$ Period of circular motion
$\omega = \frac{v}{r} = \frac{2\pi}{T}$ Angular velocity

Frequently asked questions

A 2 kg ball moves at 6 m/s in a circle of radius 3 m. What centripetal force is required?: The correct answer is: 24 N. F = mv²/r.
If you double the speed while keeping radius fixed, how does the centripetal force change?: The correct answer is: It quadruples. F ∝ v² — doubling speed quadruples force.
A car rounds a flat curve of radius 50 m at 20 m/s. What friction force is needed? (m = 1200 kg).: The correct answer is: 9,600 N. Friction provides centripetal force: f = mv²/r.