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

Distance traveled after applying brakes is given as 30 complete revolutions.
Distance = circumference x 30 = 2x3.14x0.8x30 = 150.72m
v^2= u^2 - 2as
u^2= 2as
a= u^2/2s
a= 22.2^2/(2x150.72)
a= 1.63 m/s^2 is the deceleration.
80kmph is 22.2 mps
linear acc = angular acc x radius
angular acc = 1.63/0.8 = 2.0375 rad/s^2