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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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