Question

An automobile travelling at 80 km hr−1

has tyres of radius 80 cm. On applying brakes,

the car is brought to a stop in 30 complete turns of the tyres. What is the magnitude of

the angular acceleration of the wheels? How far does the car move while the brakes are

applied?

Answer 1

u = 80 kmph = 80 * 5/18 = 200/9 m/s
radius r = 80 cm = 0.80 m
Distance traveled = 30 rotations = 30 * 2 π r = 48 π m

Initial angular velocity = ω0 = u/r = 200/9 * 1/0.80 = 200/7.2 = 250/9  rad/s
final angular velocity = ω1 = 0  stopped
Ф = total angle turned = 30 turns * 2π rad/turn = 60π rad

α = angular acceleration
   ω1² = ω0² + 2 α Ф
  0 = (250/9)² + 2 α * 60 π
  α = - 2.046 rad/sec²