Class 11 NEET Physics System of Particles and Rotational Motion

Here, Speed of the automobile,
v=54kmh−1=54×‌

5

18

ms−1=15ms−1
Radius of the wheel of the automobile, R=0.45m
Moment of inertia of the wheel about its axis of rotation, I=3‌kg‌m2
Time in which the vehicle brought to rest, t=15 s
The initial angular speed of the wheel is
ωi=‌

v

R

=‌

15ms−1

0.45m

=‌

1500

45

rads−1=‌

100

3

rads−1
and its final angular speed is ωf=0 (as the vehicle comes to rest)
∴ The angular retardation of the wheel is
α=‌

ωf−ωi

t

=‌

0− 100 3

15s

=−‌

100

45

rads−1
The magnitude of required torque is
τ=I|α|=(3‌kg‌m2)(‌

100

45

‌rad‌ s−2)
=‌

20

3

‌kg‌m2‌ s−2=6.66‌kg‌m2‌ s−2