Answer:
16.035 revolutions
Explanation:
Part 1:
t = 6 s, f0 = 0 , f = 5 rps,
Let the number of revolutions be n1.
Use first equation of motion for rotational motion
w = w0 + α t
2 x 3.14 x 5 = 0 + α x 6
α = 5.233 rad/s^2
Let θ1 be the angle turned.
Use second equation of motion for rotational motion
θ1 = w0 t + 12 x α x t^2
θ1 = 0 + 0.5 x 5.233 x 6 x 6 = 94.194 rad
n1 = θ1 / 2π = 94.194 / 2 x 3.14 = 15 revolutions
Part 2:
f0 = 5 rps, f = 0, t = 13 s
Let the number of revolutions be n2.
Use first equation of motion for rotational motion
w = w0 + α t
0 = 2 x 3.14 x 5 + α x 13
α = - 2.415 rad/s^2
Let θ2 be the angle turned.
Use third equation of motion for rotational motion
w^2 = w0^2 + 2 x α x θ2
0 = 2 x 3.14 x 5 - 2 x 2.415 x θ2
θ2 = 6.5 rad
n2 = θ2 / 2π = 6.5 / 2 x 3.14 = 1.035 revolutions
total revolutions n = n1 + n2 = 15 + 1.035 = 16.035 revolutions
