a) Let's convert the velocity of the car into m/s:
[tex]v=65 mph= 65 mil/h \cdot (1609 m/mil)/(3600 s/h)=29.1 m/s[/tex]
Let's also convert the diameter of the wheel into meters:
[tex]d=2.5 ft=0.76 m[/tex]
The radius of the wheel is r=d/2=0.38 m, and its circumference is
[tex]p=2\pi r=2 \pi (0.38 m)=2.38 m[/tex]
Since the car is moving at 29.1 m/s, a point along the circumference of the wheel will cover 29.1 m every second, so the number of revolutions per second will be given by the total distance covered in one second divided by the length of the circumference:
[tex]N= \frac{29.1}{2.38}=12.2 rev/s[/tex]
And since there are 60 seconds in 1 minute, the number of revolutions per minute is
[tex]N=(12.2 rev/s)\cdot (60 s/min)=732 rev/min[/tex]
b) The angular speed of the wheel is equal to the ratio between the wheel velocity and its radius:
[tex]w= \frac{v}{r}=\frac{29.1 m/s}{0.38 m}=76.6 rad/s[/tex]
and converting into rad/min, we get
[tex]w=(76.6 rad/s)\cdot 60=4596 rad/min[/tex]
