Question

(a) Calculate the linear acceleration of a car, the 0.280 m radius tires of which have an angular acceleration of 15.0 rad/s2. Assume no slippage. (m/s2)
(b) How many revolutions do the tires make in 2.50 s if they start from rest? (rev)
(c) What is their final angular velocity? (rad/s)
(d) What is the final velocity of the car? (m/s)

Answer 1

a. Circumference=pi*2r = 3.14 0.560=1.76
m.
a=15rad/s^2 * 1.76m/6.28rad = 4.20 m/s^2

b. V = a*t = 4.20m/s^2 * 2.50s=10.51 m/s
d = 0.5a*t^2 = 0.5*10.51*2.5^2 = 32.84 m
Revs = 32.84m * 1rev/1.76m = 18.7

c. V = 18.7rev/2.5s * 6.28rad/rev = 46.9
rad/s.

d. V = 46.9rad/s * 1.76m/6.28rad = 13.14
m/s.

Answer 2

Correction:
b. d=0.5a*t^2 = 0.5*4.20*2.5^2=13.125 m
Revs = 13.125m * 1rev/1.76m = 7.46

c. V = 7.46rev/2.5s * 6.28rad/rev=18.73
rad/s.

d. V=18.73rad/s * 1.76m/6.28rad=5.25m/s.