First slide

Dynamics of rotational motion about fixed axis

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 $m^{2}$ . If the vehicle is brought to rest in 15 s, the magnitude of average torque transmitted by its brakes to the wheel is

Moderate

A

2.86 $kg m^{2} s^{- 2}$
B

6.66 $kg m^{2} s^{- 2}$
C

8.58 $kg m^{2} s^{- 2}$
D

10.86 $kg m^{2} s^{- 2}$

Solution

Velocity of the automobile
v = 54 $\times \frac{5}{18} = 15 m / s$
$ω_{o} = \frac{v}{R} = \frac{15}{0.45} = \frac{100}{3} rad / s$
So angular acceleration
$α = \frac{∆ ω}{t} = \frac{ω_{f} - ω_{o}}{t} = - \frac{100}{45} rad / s^{2}$
So, torque $Iα = 3 \times \frac{100}{45} = 6.66$ $kg m^{2} s^{- 2}$

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