So as I was chugging along on the Rotational Motion WebAssign I was startled to notice a seemingly coincidental relationship between my givens and my answer. But after, procrastinating longer than is healthy, trying it with other numbers, the relationship was consistent.
This pertains to question 2 on the WebAssign. I found that, for a record on a turntable with an initial rpm that slows with a constant angular acceleration until rest in time t in minutes, the number of revolutions the record makes before stopping x = (rpm)(t)/2.
So if, when the turntable is shut off, the record is rotating at 100 rpm and comes to a stop in 24 seconds or 0.4 minutes, the record will make (100)(0.4)/2 = 20 revolutions before coming to rest. You can take a step further to find the angular displacement θ by multiplying by 2π . From this we get θ = (rpm)(t)(π)
I am wondering whether there is a clear derivation and reason for this. After linking it to θ, I think I know why it works and makes sense sorta. It's finding an average. Really it should be Δrpm. It's still a little fuzzy to me.
Can you clear it up?