Question 648: Centre of Mass and Rotational Motion

Question

An automobile moves on a road with a speed of 54 km h$$-$$1. The radius of its wheels is 0.45 m and the moment of inertia of the wheel about its axis of rotation is 3 kg m2. If the vehicle is brought to rest in 15 s, the magnitude of average torque transmitted by its brakes to the wheel is

Accepted Answer

Here, Speed of the automobile,
$$v = 54\,km{h^{ - 1}} = 54 	imes {5 \over {18}}m{s^{ - 1}} = 15m{s^{ - 1}}$$
Radius of the wheel of the automobile, R = 0.45 m
Moment of inertia of the wheel about its axis of
rotation, I = 3 kg m
2
Time in which the vehicle brought to rest, t = 15 s
The initial angular speed of the wheel is
$${\omega _i} = {v \over R} = {{15m{s^{ - 1}}} \over {0.45\,m}} = {{1500} \over {45}}rad\,{s^{ - 1}} = {{100} \over 3}rad\,{s^{ - 1}}$$
and its final angular speed is $${\omega _f}$$ = 0 (as the vehicle comes to rest)
$$ 	herefore $$ The angular retardation of the wheel is
$$\alpha  = {{{\omega _f} - {\omega _i}} \over t} = {{0 - {{100} \over 3}} \over {15\,s}} =  - {{100} \over {45}}rad\,{s^{ - 1}}$$
The magnitude of required torque is
$$	au  = I\left| \alpha  ight| = \left( {3kg\,{m^2}} ight)\left( {{{100} \over {45}}rad\,{s^{ - 2}}} ight)$$
$$ = {{20} \over 3}kg\,{m^2}{s^{ - 2}} = 6.66\,kg\,{m^2}{s^{ - 2}}$$

Answer

10.86 kg m2 s$$-$$2

Answer

2.86 kg m2 s$$-$$2

Answer

6.66 kg m2 s$$-$$2

Answer

8.58 kg m2 s$$-$$2

Centre of Mass and Rotational Motion

An automobile moves on a road with a speed of 54 km h$-$1. The radius of its wheels is 0.45 m and the moment of inertia of the wheel about its axis of rotation is 3 kg m2. If the vehicle is brought to rest in 15 s, the magnitude of average torque transmitted by its brakes to the wheel is

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