Question

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

Answer 1

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.

Answer 2

angular speed w= radians/time...
distance=radius * radians
velocity=distance /time
so w=velocity*radians..
now substitute the values and get the result

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

right sry.

Answer 7

correct me if i'm wrong

\[180mile/1 hr * 1rev/2\pi * O.25 = 45/2\pi rev/hr\]

Answer 8

What happened to the .25?

Answer 9

.25 is the radius r

Answer 10

I understand. But 180/.25 is NOT 45

Answer 11

180 * .25 = 45

Answer 12

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

Answer 13

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

Answer 14

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