you are driving your 1200kg car at a speed of 400 mph You st

you are driving your 1200kg car at a speed of 40.0 mph. You step on your brakes and your car comes to a stop in 7.00s. Each car tire has a radius of 0.300m. a) Calculate the angular velocity of one of the tires before you started braking b) Calculate the angular deceleration of one of the tires. c) How many revolutions does a tire make before coming to a stop (Answers: a) 59.6rad/s, b) -8.51rad/s^2, c) 33.2rev)

Solution

As we know, 1 mile per hour = 0.447 m/s

Therefore, 40 mile per hour = 40x0.447 = 17.88 m/s = v

(a) Radius of the tire, r = 0.30 m.

So, angular velocity, w = v/r = 17.88/0.30 = 59.6 rad/s

(b) Applying the formula -

w1 = w + a * t

where, a is the angular accleration.

So, 0 = 59.6 + a*7.0

=> a = - 59.6/7 = - 8.51 rad/s^2

(c) Let \'s\' be the total revolution before the tire come to stop.

So, s = w*t + (1/2)*a*t^2 = 59.6*7 - (1/2)*8.51*7^2 = 417.2 - 208.495 = 208.70 radian

Now convert this in revolution.

For this simply divide the result by (2*pi)

So the answer is  208.70 / (2*pi) = 33.2 revolutions.