## anonymous 4 years ago A race car is driven around a circular track at a constant speed of 180mph. If the diameter is 1/2 mile, what is the angular speed of the car? Express your answer in revolutions per hour. The formula for angular speed is w=theta (in radians)/time

1. barrycarter

If the diameter is 1/2 mile, the circumference is Pi times 1/2 mile, or about 1.5708 miles. Since the driver goes 180 miles in one hour, he makes 180/1.5708 revolutions per hour or about 114.59 revolutions per hour.

2. anonymous

3. Mertsj

$\frac{180 mi}{1hour}\times\frac{1revolution}{.5\pi mi}=114.59 \frac{rev}{hour}$

4. PaxPolaris

$(angular\ speed)\ w = (radians\ per\ mile\ of\ Circumference ) \times (speed)$$(radians\ per\ mile\ of\ Circumference )= {(2 \cancel \pi ) radians \over \left( \cancel \pi \cdot \frac12 \right) miles} = 4 radians/mile$ $w = {4 radians \over \cancel{mile}}\times{180\ \cancel {miles} \over hour} = 720{ radians \over hr} = \large 12 {radians \over \min} =\huge 0.2 {radians \over \sec}$

5. Mertsj

Remember pax, the directions specified that the answer be in revolutions per hour.

6. PaxPolaris

right sry.

7. anonymous

correct me if i'm wrong $180mile/1 hr * 1rev/2\pi * O.25 = 45/2\pi rev/hr$

8. Mertsj

What happened to the .25?

9. anonymous

10. Mertsj

I understand. But 180/.25 is NOT 45

11. anonymous

180 * .25 = 45

12. Mertsj

$\frac{180 mile}{1 hr}\times\frac{1rev}{2\pi(.25)}=\frac{180}{2\pi)(.25)}$

13. Mertsj

Exactly my point. The .25 is in the denominator and you must divide by it.

14. Mertsj

$\frac{180}{2\pi(.25)}=\frac{180}{1.570796}=114.59$