anonymous
  • anonymous
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
Mathematics
katieb
  • katieb
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barrycarter
  • 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.
anonymous
  • anonymous
angular speed w= radians/time... distance=radius * radians velocity=distance /time so w=velocity*radians.. now substitute the values and get the result
Mertsj
  • Mertsj
\[\frac{180 mi}{1hour}\times\frac{1revolution}{.5\pi mi}=114.59 \frac{rev}{hour}\]

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PaxPolaris
  • PaxPolaris
\[(angular\ speed)\ w = (radians\ per\ mile\ of\ Circumference ) \times (speed)\]\[ (radians\ per\ mile\ of\ Circumference )= {(2 \cancel \pi ) radians \over \left( \cancel \pi \cdot \frac12 \right) miles} = 4 radians/mile\] \[w = {4 radians \over \cancel{mile}}\times{180\ \cancel {miles} \over hour} = 720{ radians \over hr} = \large 12 {radians \over \min} =\huge 0.2 {radians \over \sec}\]
Mertsj
  • Mertsj
Remember pax, the directions specified that the answer be in revolutions per hour.
PaxPolaris
  • PaxPolaris
right sry.
anonymous
  • anonymous
correct me if i'm wrong \[180mile/1 hr * 1rev/2\pi * O.25 = 45/2\pi rev/hr\]
Mertsj
  • Mertsj
What happened to the .25?
anonymous
  • anonymous
.25 is the radius r
Mertsj
  • Mertsj
I understand. But 180/.25 is NOT 45
anonymous
  • anonymous
180 * .25 = 45
Mertsj
  • Mertsj
\[\frac{180 mile}{1 hr}\times\frac{1rev}{2\pi(.25)}=\frac{180}{2\pi)(.25)}\]
Mertsj
  • Mertsj
Exactly my point. The .25 is in the denominator and you must divide by it.
Mertsj
  • Mertsj
\[\frac{180}{2\pi(.25)}=\frac{180}{1.570796}=114.59\]

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