Quandaries and Queries


I am in 12th grade and taking a pre-calculus course. I'm having a problem with angular speed:

A 4 inch pulley on a motor makes 1500 revolutions/minute. It is connected to an 8 inch saw blade.

a. Find the angular speed of the pulley in radians/minute
b. Find the angular speed of the saw in radians/ minute

We were taught to use theta/ time. But if I use this formula I get the same answer for both questions which I know isn't right.

Please let me know what to do??



Hi Rachel,

The question I have is "How is the pully connected to the saw balde?" On my saw there is a pulley attached to the motor (your 4 inch pulley) and a shaft through the blade that is attached to a second pulley. There is a belt between the two pulleys as in the diagram.

If the two pulleys are same size then the saw blade and the motor will have the same number of revolutiions per minute and thus the 4 inch pulley and the saw blade will have the same angular speed (your answer). If, for example, the second pulley is half as large (a 2 inch pulley) then its circumference will be half the circumference of the 4 inch pulley, and it will rotate at 2x1500=3000 revolutions per minute. Thus in this case the angular speed of the saw blade will be twice the angular speed of the 4 inch pulley.



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