Question

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

Solution

## Initial linear velocity:$$v_1=54 km/h$$$$=54\times\dfrac{5}{18}$$$$=15 m/s$$Initial angular velocity:$$ω1=\dfrac{v_1}{r}$$$$=\dfrac{15}{0.35}$$$$=42.9 rad/s$$Final angular velocity:$$ω_2=0$$Angular acceleration:$$\alpha=\dfrac{ω_2−ω_1}{t}$$$$=\dfrac{0−42.9}{15}$$$$=−8.57 rad/s^2$$Torque:$$\tau =I\alpha$$$$=3\times−8.57$$$$=−25.7 N⋅m$$Physics

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