Question

An automobile moves on a road with a speed of $54km{h}^{-}$. The radius of its wheels is $0.3m$. What is the average negative torque transmitted by its breaks to a wheel if the vehicle is brought too rest in $15s$? The moment of inertia of the wheel about the axis of rotation is $3kg{m}^2$.

Answer 1

Initial linear velocity:

$v_1=54km/h$

$=54\times \frac{5}{18}$

$=15m/s$

Initial angular velocity:

$\omega 1=\frac{v_1}{r}$

$=\frac{15}{0.35}$

$=42.9rad/s$

Final angular velocity:

${\omega }_2=0$

Angular acceleration:

$\alpha =\frac{{\omega }_2-{\omega }_1}{t}$

$=\frac{0-42.9}{15}$

$=-8.57rad/s^2$

Torque:

$\tau =I\alpha$

$=3\times -8.57$

$=-25.7N\cdot m$