Question

a car accelerates from rest until it reaches a velocity of 20m/s in 15s.if the radius of the cars wheels is 0.4.,calculate the angular acceleration of its wheel during that 15s and calculate the number of revolution made during that 15s.

Answer 1

$$\alpha=\frac{a}{r}=\frac{v}{rt}=\frac{20}{(15)(0.4)}=3.33\frac{rad}{s^2}$$ $$(2\alpha \theta)=\omega^2\\2\pi n(2\alpha)=\frac{v^2}{r^2}\\(2\cdot3.33)2\pi n=\frac{20^2}{0.4^2}\\n=59.7$$