During a movie shoot, a car with a stunt driver inside is lifted off the ground. The stunt driver starts the engine and sets the wheels of the car with angular speeds of ωi. The car then is brought back down onto the ground. At the moment the car wheels make contact with the ground, the speeds of the center of masses of the car wheels are zero. In the beginning, the car wheels skid on the ground and move forward. But after a short time, they begin to roll without skidding. Given that, the moment of inertia of a car wheel about the axle is I = (1/2)mR2, and the coefficient of friction between the car wheels and the ground is μ, evaluate what the final translational speed value vcm of the center of mass of a car wheel will be.
[Hint: Use Newton's second law, ∑τcm = Icmαcm, and consider that vcm = ωr only applies when the car wheels roll without skidding.]
