Question

Question #e264b

Answer 1

Velocity of the automobile `v=80"km/h"=(80xx10^3m)/(60xx60s)=200/9"m/s"`

Radius of Tyre `r=80cm =0.8m`

Initial angular velocity of wheels

`omega_0=v/r=200/(0.8xx9)"rad/s"=250/9"rad/s"`

On application of brakes the car stops in 30 complete turns. So the angular displacement of wheels `theta =30xx2pi=60pi` radian.
Final angular velocity of wheel `omega =0`

If angular acceleration be `alpha` then we can write from equation of rotational motion

`omega^2=omega_0^2+2alphaxxtheta`

Inserting values we get

`0^2=(250/9)^2+2xxalphaxx60pi`

`=>alpha=-(250xx250)/(9xx9xx120pi)~~-2"rad/"s^2`