Question

A car is moving at a speed of 72 km/hr. the diameter of its wheels is 0.5 m. If the wheels are stopped in 20 rotations by applying brakes, then angular retardation produced by the brakes is

• A. $-25.5{\text{rad/s}}^2$
• B. $-29.5{\text{rad/s}}^2$
• C. $-33.5{\text{rad/s}}^2$
• D. $-45.5rad/s^2$

Answer 1

The correct option is A $-25.5{\text{rad/s}}^2$

Given speed of the vehicle=$72㎞/hr$

=$72\times \frac{5}{18}=20m/s$

radius of the wheel =$\frac{0.5}{2}=0.25$

initial angular velocity $\left({\omega }_0\right)=\frac{20}{0.25}=80rad/s$

angle covered after applying brakes=$20\times 2\pi =40\pi$

let the angular retardation be $-\alpha rad/s^2$

final angular momentum $\omega$=0

putting formula ${\omega }^2={{\omega }_0}^2-2\alpha \theta$

$\Rightarrow 0={{\omega }_0}^2-2\times \alpha \times \theta \Rightarrow {{\omega }_0}^2=2\times \alpha \times \theta \Rightarrow {80}^2=2\times \alpha \times 40\times \pi \Rightarrow \alpha =\frac{{80}^2}{80\times \pi }\Rightarrow \alpha =\frac{80}{\pi }$

putting the value of $\pi =3.14$

$\alpha =25.47rad/s^2$

so retardation is $-25.477\cong -25.5$ $rad/s^2$