Question

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

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

Answer 1

Answer: (D)

Here : Speed of car = $72km/hr$
$=\frac{72\times 5}{18}=20cm/s$
Diameter of each wheel $=\frac{0.5}{2}m$
Number of rotation $=20$
The relation for angular speed is
$\omega =\frac{v}{r}=\frac{20}{0.25}=80rad/\sec$
Angular displacement
$Q_1=2\pi \times 20=40\pi rad$
The relation for angular retardation is given by
${\omega }^2={\omega }_0^2+2aQ$
$0=(80{)}^2+2a(40\pi )$
$a=\frac{(80{)}^2}{80\pi }=-25.5rad/s^2$