Question

A car is moving at a speed of 72 Km/hour. The diameter of its wheels is 50 cm. If its wheels come to rest after 20 rotations as a result of the application of brakes, then the angular retardation produced in the car will be

• A. $-25.5$ $radians/s^2$
• B. $0.25$ $radians/s^2$
• C. $2.55$ $radians/s^2$
• D. 0

Answer 1

Answer: (A)

$-25.5$ $radians/s^2$

Initial speed, $v=72$ $km/h$

$⟹v=\frac{72\times {10}^3}{3600}$

$⟹v=20$ $m/s$

Distance, $2r=50$ $cm$

$⟹r=25\times {10}^{-2}$ $m$

Angular displacement, $\theta =20\times 2\pi$

$⟹\theta =40\pi$ $rad$

Initial angular velocity, $\omega =\frac{v}{r}$

$⟹\omega =\frac{20}{25\times {10}^{-2}}$

$⟹\omega =\frac{4}{5}\times {10}^2$

$⟹\omega =80$ $rad/s$

Final angular velocity, ${\omega }^{\prime }=0$ $rad/s$

From kinematics:

${\omega }^{\prime 2}-{\omega }^2=2\alpha \theta$ (where $\alpha$ is angular acceleration)

$⟹0-6400=2\alpha \times 40\pi$

$⟹\alpha =\frac{-6400}{80\pi }$

$⟹\alpha =-25.5$ $rad/s^2$