Centripetal Force and Acceleration
Q1
- On a ride at a theme park, riders are strapped unto seats attached to the edge of a horizontal wheel of diameter 8.5m. The wheel rotates 15 times per minute. What is the force felt by a rider of mass 60kg?
- \(\omega=2\pi f\)
- \(2\pi \times\frac{15}{60}=\frac{1}{2}\pi\)
- \(m\omega^2r=F\)
- \(60\times \left( \frac{1}{2}\pi \right)^2\times \frac{8.5}{2}=629.19N\)
Q2
- A planet has radius \(r\) and constant centripetal acceleration \(a\). How long for the planet to go round the star 3 times?
- \(\omega=\frac{2\pi}{T}\)
- \(a=\omega^2r\)
- \(\omega=\sqrt{ \frac{a}{r} }\)
- \(T={2\pi}{\sqrt{ \frac{a}{r} }}\)
- \(3T=6\pi \sqrt{ \frac{a}{r} }\)
Q3a
- Calculate the centripetal acceleration of a car in radius 56.8 and linier speed 31.1m/s
- \(a=\frac{v^2}{r}\)
- \(\frac{31.1^2}{56.8}=17.028\)
Q3b
- \(\frac{1}{4}F\)