Conceptional question regarding units in linear speed (Quick Question- No calcul

Question

Conceptional question regarding units in linear speed (Quick Question- No calculation needed - Easy points)

Hi, I just have a simple question regarding the units in calculating linear speed using the equation: v = rw

I have attached a problem for reference, but it is already solved.

Setting up the equation:

v = rw

v = (.240 m) x (650 radians/s)

v = 156 m/s

Units are m/s, but at what point do radians cancel out? Maybe I am missing something simple...

Thank you for your help in advance! Best answer will receive points right away!

10.00 points 1 out of 3 attempts A trimmer for cutting weeds and grass near trees and borders has a nylon cord of 0.240 m length that whirls about an axle at650 rad/s. What is the linear speed of the tip of the nyloin cord? 156 m/s

Explanation / Answer

w is angular speed
v is linear speed

both are speeds, so to convert from an angular speed in rad/s to a tangential speed in m/s, you multiply the angular speed by the radius of rotation,

Hence v = r*w
So we get v = 0.250m * 650rad/s
= 156 m/s

To turn through a complete circle you turn through 360 degrees of arc, or 2 pi radians of arc. They are the same thing. If the angle of arc is changing at some rate measured in radians per second then a point at the end of a radius of r meters is tracing out a circular arc at a rate of r meters per second.

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