On a flat road
Circular Motion - OCR A-Level Physics
- On a flat road: friction between tyres and road provides centripetal forceThe resultant force directed towards the centre of a circular path that causes an object to move in a circle. It is not a separate force but the net force providing circular motion.. Maximum speed: $v_{max} = \sqrt{\mu g r}$ where $\mu$ is the coefficient of friction.
- On a banked track: the horizontal component of the normal reaction provides centripetal forceThe resultant force directed towards the centre of a circular path that causes an object to move in a circle. It is not a separate force but the net force providing circular motion.. At the design speed, no friction is needed.
- For a banked track at angle $\theta$ with no friction: $\tan\theta = v^{2}/(rg)$.
- If the car goes faster than the design speed, friction acts down the slope (towards the centre). If slower, friction acts up the slope.
- Banking is used on motorway curves, velodromes, and aircraft turns to reduce reliance on friction.
Worked Example
A car travels around a flat circular bend of radius 50 m. The coefficient of friction is 0.80. Calculate the maximum speed.
Show Solution
1
Friction provides centripetal forceThe resultant force directed towards the centre of a circular path that causes an object to move in a circle. It is not a separate force but the net force providing circular motion.
$F_{friction} = F_{centripetal}.$
2
$\mu mg = mv^2/r.$
3
Cancel m
$v^2 = \mu gr.$
4
$v = \sqrt{0.80 \times 9.81 \times 50}.$
5
$v = \sqrt{392.4} = 19.8 \text{ m s}^{-1}$.
6
$v \approx 20 \text{ m s}^{-1}$ (about 44 mph).
Answer
$v_{max} \approx 20 \text{ m s}^{-1}$