Answer to Question #114153 in Mechanics | Relativity for Feker

Question

An automobile traveling at 80.0km/hour has tires of 75.0cm diameter
A, what is the angular speed of the tires about their axles?
B, if the car is brought to a stop uniformly in 30.0 complete turns of the tires (without skidding). What is the magnitude of the angular acceleration of the wheels.
C, how far does the car move during the parking?

Answer 1

a)

$$\omega=\frac{v}{r}=\frac{80}{3.6\cdot 0.75}=29.6\frac{rad}{s}$$

b)

$$\omega^2=2\alpha \theta\to 29.6^2=2(2\pi)(30)\alpha$$

$$\alpha =2.32\frac{rad}{s^2}$$

c)

$$d=\theta r=(2\pi)(30)0.75=141\ m$$