Answer: 35 revolutions.
Explanation: it has been stated in the question that the motion is of a constant angular acceleration, thus newton's laws of motion for rotational motion is valid.
Let
ω = final angular speed (rev/s)
ω' = initial angular speed (rev/s)
t = time taken (s)
α = angular acceleration (rev/s²)
θ = angular displacement (rev)
Since the object starts from rest, ω' = 0 and from the question ω =5rev/s and t= 8s
We need to get the value of the constant angular acceleration α
This can be gotten using the formulae
ω = ω' + αt but ω' =0, thus we have that
ω = αt.
α = ω/t = 5/8
Thus α = 0.625rev/s².
This is a constant value as stated in the question and will be used at any point in the motion.
Let us calculate the angular displacement for this time period using the formula
θ =ω't + 1/2αt²
But ω' = 0, thus
θ = 1/2αt²
Thus
θ = 1/2 * 0.625 * 8²
= 1/2 * 0.625 * 64
Thus θ =20 revolution.
For the second phase of motion, the washer has being switched off and the body is coming to rest with the same value of angular acceleration but with a negative value because the motion is reducing (-0.625m/s²) at time t = 12s.
Since the body is coming to rest, ω = 0 and ω' = 5rev/s t= 12s and α=- 0.625m/s²
To get the value of angular displacement at t=12s, we use the formulae below
θ =ω't + 1/2αt²
ω' =5rev/s α= - 0.625m/s² and t= 12s.
θ = (5*12) + 1/2 (-0.625)*12²
= 60 - 1/2 * 0.625* 144
= 60 - 0.625 * 72
= 60 - 45
= 15 revolution. (this is a lower revolution compared to the first because the body is coming to rest thus making it move slow)
The total angular displacement is a total of 20 + 15 = 35 revolutions.