Asafety device brings the blade of a power mower from an initial angular speed of w1 to rest in 5.00 revolutions. at the same constant accelerations, how many revolutions would it take the blade to come to rest from an initial angular speed w3 that was three times as great, w3 = 3w1?

Hello!

If the acceleration is a constant omega prime is 3times omega inital then it would take 15revs to stop. 3 times the revolutions because everything is held as a constant and the only change is omega. 

Theta final=Theta initial + omega initial * t +1/2at^2

Theta is revs and this is what you want to find. so lets set it up and check. assuming everything stays constant BUT omega, then we can treat everything else in the equation as a one, or essentially disregard them. So we see a linear relationship to revolutions or theta, meaning whatever factor omega is increased or decreased then if everything else is a constant then revolutions will change by the same factor. Omega is angular speed or how fast something is spinning on an axis of rotation. 

Hope this explanation helps. Any questions please ask! Thank you so much!

Hypothesis. why don’t you know this? i learned this stuff in like 5th grade