Just need to make sure im doing this right...

Question

anonymous · Answer

Determine the linear velocity of a point rotating at an angular velocity of 15pi radians per second at a distance of 12 feet from the center of the rotating object.

anonymous · Answer

$$v=r \omega $$

anonymous · Answer

so the equation would be 
v=12(15pi)

anonymous · Answer

and so then the linear velocity would be
565.5 ft/s

amistre64 · Answer

how long is the track its running on?  what the circumference of your circle?

anonymous · Answer

@amistre64 well i dont think circumference matters when it comes to linear velocity...

amistre64 · Answer

it should, thats the distance we travel in a 2pi rotation

if we have 15pi rotations a second.

15/2 = 7.5 circumference traveled per second is a linear speed

amistre64 · Answer

if you have a wheel that 1 foot in circumference, and you spin the wheel once per second,  youve traveled 1 foot in 1 second,  you are going a linear speed of 1ft/sec

right?

anonymous · Answer

its actually 15pi RADIANS... not revolutions. so we dont have to convert anything i think

amistre64 · Answer

if you have a wheel that is 10 feet in circumference, and spin it once per second,  youve traveled 10 feet in a second.  your 

15pi radians is 7.5 rotations of a unit circle.

your angle is changeing by 15 pi each second.  thats not a linear dimension, its angular

amistre64 · Answer

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which point has traveled the longer distance in the same amount of time?