What is the total rotational kinetic energy of the wheels?

[brncsfns5621]

A 50kg rider on a moped of mass 75kg is traveling with a speed of 20 m/s. Each of the two wheels of the moped has a radius of 0.2m and a moment of inertia of 0.2 kg*m^2. What is the total rotational kinetic energy of teh wheels?

KEr = 1/2Iw^2
= 1/2(.02)(20)^2
= 4
Two wheels = 2 *4 = 8 Joules

I think I am wrong as the angular velocity (w) has to be in rad/s. For some reason, I can not figure out how to get that. What is the formula for w?

 

[Doc Al]

Yes, that formula requires angular speed, not linear speed. They are related by: v = wr.

(A complete circle, one circumference, is equivalent to 2 \pi radians.)

 

[NateTG]

Yeah, you're using an incorrect value for \omega.

If you're confused by the radians, it might be helpful to figure out how many degrees per second the wheels are turning, and then use the conversion:
1 \rm{degree}=\frac{\pi}{180} \rm{radians}

 

[brncsfns5621]

thanks. I knew I was forgetting something. It just didn't look right.