Thread: Linear/Angular Speed

The circular blade of a saw has a diameter of 7.5 inches and rotates 2400 revolutions per minute

a). Find the angular speed in radians per second
b). Find the linear speed of the saw teeth (in feet per second) as they contact the wood being cut

a). So angular speed= Theta/time (then I solved like this)
so I take 2400/60 to get revolutions per second so its 40 revolutions per second

Multiply 40 by 2(pi) for one complete revolution to get 80(pi)

Am I doing this correct. I think it is right because this is what the example shows me. 40 is theta because why? Why is it not the arc length?

b). for linear will I take 40 and multiply it by 3.75 then divide that by 60? to get 2.5(pi)

Originally Posted by IDontunderstand

The circular blade of a saw has a diameter of 7.5 inches and rotates 2400 revolutions per minute

a). Find the angular speed in radians per second
b). Find the linear speed of the saw teeth (in feet per second) as they contact the wood being cut

a). So angular speed= Theta/time (then I solved like this)
so I take 2400/60 to get revolutions per second so its 40 revolutions per second

Multiply 40 by 2(pi) for one complete revolution to get 80(pi)

Am I doing this correct. I think it is right because this is what the example shows me. 40 is theta because why? Why is it not the arc length?

b). for linear will I take 40 and multiply it by 3.75 then divide that by 60? to get 2.5(pi)

a) this is just a conversion ...

2400 rpm = 40rps = 80pi rad/s

b) linear speed = (radius)(angular speed) ... angular speed has to be in radians per unit time

v = rw = (7.5/12)(80pi) = 50pi ft/s