Answer:
The angular velocity is 6.72 π radians per second
Step-by-step explanation:
The formula of the angular velocity is ω = [tex]\frac{v}{r}[/tex] , where v is the linear velocity and r is the radius of the circle
The unit of the angular velocity is radians per second
∵ The diameter of the tire is 25 inches
∵ The linear velocity is 15 miles per hour
- We must change the mile to inch and the hour to seconds
∵ 1 mile = 63360 inches
∵ 1 hour = 3600 second
∴ 15 miles/hour = 15 × [tex]\frac{63360}{3600}[/tex]
∴ 15 miles/hour = 264 inches per second
Now let us find the angular velocity
∵ ω = [tex]\frac{v}{r}[/tex]
∵ v = 264 in./sec.
∵ d = 25 in.
- The radius is one-half the diameter
∴ r = [tex]\frac{1}{2}[/tex] × 25 = 12.5 in.
- Substitute the values of v and r in the formula above to find ω
∴ ω = [tex]\frac{264}{12.5}[/tex]
∴ ω = 21.12 rad./sec.
- Divide it by π to give the answer in terms of π
∴ ω = 6.72 π radians per second
The angular velocity is 6.72 π radians per second
