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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
  • \(\frac{1}{4}F\)
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