Q. A car is moving at a speed of $72\ km/hr$. The radius of its wheels is $0.25\ m$. If the wheels are stopped in 20 rotations by applying brakes, then angular retardation produced by the brakes is
A) $- 25.5\ rad/s^{2}$
B) $- 29.5\ rad/s^{2}$
C) $- 33.5\ rad/s^{2}$
D) $- 45.5\ rad/s^{2}$
Explanation
(a) $\omega_{0} = \frac{v}{r} = \frac{72 \times 5/18}{0.25} = 80rad/s$
$\omega = 0,\ \theta = 2\pi n = 2\pi \times 20 = 40\pi\ rad$
Substituting these value in equation
$\omega^{2} = \omega_{0}^{2} + 2\alpha\theta$
$\Rightarrow \alpha = - \frac{\omega_{0}^{2}}{2 \times \theta} = - \frac{80 \times 80}{2 \times 40\pi} = - 25.5rad/s^{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.