physics, angular stuff?

Question

An automobile traveling at 50.0 km/h has tires of 80.0 cm diameter.


(a) What is the angular speed of the tires about their axles?
rad/s

(b) If the car is brought to a stop uniformly in 25.0 complete turns of the tires (without skidding), what is the magnitude of the angular acceleration of the wheels?
rad/s2

(c) How far does the car move during the braking?
m

Answer 1

Using w=v/r

=50*1000/(3600*0.8)
=17.4 rad/sec

Using
th=th0+w0*t+.5*a*t^2
th0 is zero
th=25*2*pi
157 rad
w0=17.4
0.5*a*t^2+17.4*t=157

using
w=w0+a*t
0=17.4+a*t
a=-17.4/t

plugging in above
t=157/(.5*17.4)
t=18.05s

a=-17.4/18.05

a=-0.964 rad/s^2

25 complete turns with a circumference of
pi*.8
d=25*pi*.8
d=62.8 m

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