RPM of axle from velocity of car

[picotron]

Homework Statement

I have to derive an equation that relates the rpm of an axle that is fixed to a car wheel of radius r, given the velocity of the car

subscripts: w is wheel, a is axle

Homework Equations

angular velocity of the wheel is given by

ω_wheel=2π/T=2πf=v/r_w (1)

The angular momentum of the wheel is given by

L_w=1/2 mr_w^2 ω_w (2)

The Attempt at a Solution

By using the conservation of angular momentum, I get

1/2 mr_w^2 ω_w=1/2 mr_a^2 ω_a

after cancellation I get

(r_w^2)/(r_a^2 ) ω_w=ω_a

substituting in equation (1) above yields

r_w/(r_a^2 ) v=ω_a

then converting the angular velocity of the axle into rpm by dividing the rad/s by 2π and multiplying by 60.

So, by this, the angular velocity of the axle is higher than the angular velocity of the edge of the car wheel.

Is this correct? or is the rpm of the axle the same as the rpm of the car wheel?

 

[picotron]

never mind people I've been getting myself confused.

Clearly it should just be the velocity of the car divided by the wheel radius and then converted to rpm.