Answer to Question #80527 in Mechanics | Relativity for zara

Question

An electric fan is turning at= 3:0rev/s when it is turned on, it coasts to rest int1= 18s. Assuming the deceleration is uniform, how many revolutions did it turn through while coming to rest?

Answer 1

If deceleration is uniform, so we can say, that ε=(ω-ω_0)/t=(0-3)/18=-3/18=-1/6 rev/s^2
So, the law of motion will look like φ=φ_0+ω_0 t+(εt^2)/2=3t-t^2/12. Then rotation made in t1 will be ∫_0^t1▒(3t-t^2/12)dt=3/2 〖t1〗^2-〖t1〗^3/36=3/2*〖18〗^2-〖18〗^3/36=486-162=324 revolutions