Centripetal Force | CAIE 9702 Paper 4 Notes

Paper 4

Physics9702

From acceleration to force

Newton's second law links resultant force, mass and acceleration. The resultant force has the same direction as the acceleration.
is the name for the inward resultant force in circular motion.

Definition

1 mark

Model answer: The resultant force acting towards the centre of a circular path.

F=\dfrac{mv^2}{r}

Symbols

Substitute the speed–radius acceleration into Newton's second law to obtain the force formula above.
When angular speed is given, substitute the angular-speed acceleration instead.

F=ma=m\dfrac{v^2}{r}=\dfrac{mv^2}{r}

F=ma=mr\omega^2

Worked example

A rubber stopper

A 0.20 kg rubber stopper moves at 4.0 m s⁻¹ in a circle of radius 0.50 m. Find the inward resultant force.

Substitute mass, speed and radius.
$F=\dfrac{mv^2}{r}$
$F=\dfrac{0.20\times4.0^2}{0.50}=6.4\text{ N}$

Answer

F=6.4\text{ N towards the centre}

Your turnQuick check

A 0.30 kg object moves in a circle of radius 0.80 m at angular speed 5.0 rad s⁻¹. Find the inward resultant force.

Show worked answer

Use the angular-speed form and substitute the values.

F=mr\omega^2

F=0.30\times0.80\times5.0^2

F=6.0\text{ N}