Centripetal acceleration and centripetal force
a = v²/r = ω²r = 4π²r/T², the net force towards the centre, what supplies it, and why “centrifugal force” is a myth.
Cut the string on a swinging ball and it does not fly outwards. It flies off in a straight line. So what was the string doing?
A body moves at 4.0 m s⁻¹ on a circle of radius 2.0 m. Its centripetal acceleration is…
A 0.50 kg ball moves at constant speed in a circle of radius 0.80 m with period 1.0 s. The centripetal force is…
The speed of a body in circular motion is doubled (same radius). The centripetal force becomes…
The string holding a ball in a horizontal circle breaks. The ball then moves…
In uniform circular motion the work done by the centripetal force in one revolution is…
A car goes round a flat circular bend at constant speed. State the force that provides the centripetal force and explain why the passengers seem to be “thrown outwards”.
ω = …
The magnetic force on a moving charge is…
Key points
- • a = v² / r = ω²r = 4π²r / T², towards the centre.
- • F = ma = mv² / r = mω²r = 4π²mr / T²: the resultant force towards the centre.
- • It is perpendicular to the velocity: it changes the direction, not the speed, and does no work.
- • There is no outward centrifugal force in an inertial frame.
Formulas
- a = v²/r = ω²r = 4π²r/T²
- F = mv²/r = mω²r
Key terms
- Centripetal force :
- the resultant force towards the centre that makes a body move in a circle
Common errors
- • Drawing a separate “centripetal force” arrow on the diagram
- • Adding an outward centrifugal force
- • Forgetting the square on v or T