Question

A car of mass 8000kg moves in a circular path of 100m with a linear velocity of 50m/s.Calculate the i) Angular velocity ii) Angle the tyre makes with the ground iii) condition for skidding for u(coefficient of friction)= 0.5?

Answer 1

(i) the angular velocity

$$\omega=v/R\\ =\rm (50\: m/s)/(100\: m)=0.5\: rad/s$$

(ii) the angle the tyre makes with the ground

$$\theta=\tan^{-1}\frac{v^2/(gR)-\mu}{1+\mu}$$ $$\theta=\tan^{-1}\frac{50^2/(9.8*100)-0.5}{1+0.5}=54^\circ$$

(iii) the condition for skidding

$$v>v_{\max}=50\:\rm m/s$$ $$\theta<54^\circ$$