# Frame of reference of bicycle rider

1. May 3, 2015

### Alex_Neof

1. The problem statement, all variables and given/known data
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.

2. Relevant 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):

$I=M R^2$

3. The attempt at a solution

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.

Last edited: May 3, 2015
2. May 3, 2015

Looks right.

3. May 3, 2015

Thank you!