An automobile traveling at 600 kmh has tires of 850 cm diame

An automobile traveling at 60.0 km/h has tires of 85.0 cm diameter, What is the angular speed of the tires about their axles? If the car is brought to a stop uniformly in 40.0 complete turns of the tires [without skidding). what is the magnitude of the angular acceleration of the wheels? Mow far does the car move during the braking?

Solution

(a) angular speed = speed/radius

speed = 60x5/18 = 16.67 m/s

angular speed = 16.67 / (0.85/2) = 39.22 rad/s

(b) angular distance in 40 turns = 2 x pie x 40 = 251.33 rad

Final angular speed = zero

From equation of kinematics

Angular accleration = -(Initial angular speed)²/(2xAngular distance) = (39.22)²/ (2 x 251.33) = - 3.06 rad/s²

(c) Distance travelled = (Intial speed)²/ (2xlinear accleration)

linear accleration = (0.85/2)(-3.06) = -1,3 m/s²

distance travelled = (16.67)²/(2x1.3) = 106.88 meters