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Alex_Neof
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Homework Statement
A wheel of a bicycle weighs 1 kg, all of which is at the rim. The diameter of the wheel is 0.7 m. If the bicycle is ridden at the speed of 3.5 m s–1, then in the frame of
reference of the rider:
i) Calculate the angular speed ω of the wheel.
ii) Calculate the momentum of the rim, p.
iii) Calculate the angular momentum of the wheel.
iv) Calculate the kinetic energy of the wheel.
Homework Equations
## v = {\omega} r ##
## \rho = mv ##
## L=I\omega ##
## Kinetic\ Energy = \frac{1}{2} m v^2 + \frac{1}{2} I \omega ^2##
Moment of Inertia of a hoop (for the wheel, ignoring the spokes):
## I=M R^2 ##
The Attempt at a Solution
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i) ## \frac {v}{r} = 10\ rad\ s^{-1}##
ii) ## 0 \ {kg}\ m\ s^{-1}## (Since in the frame of reference of the rider, there is no linear translation?)
iii) ## L=(M R^2) \omega ##
##(1) (0.35)^2 (10) = 1.225 {kg}\ m^2 ##
iv) ##Kinetic\ Energy = \frac{1}{2} I \omega ^2## Ignoring the linear term again.
##Kinetic\ Energy = (0.5) (0.35) ^2 (10)^2 = 6.125 J ##
Is this correct?
Thank you.
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