Answer:
(a) α = - 1000 rad/s²
Negative sign represents deceleration.
(b) θ = 3581 rotations
(c) L = 1800 m
(d) a = - 80 m/s²
Explanation:
(a)
using First equation of motion for angular motion:
ωf = ωi + αt
where,
ωf = Final Angular Speed = 2000 rad/s
ωi = Initial Angular Speed = 7000 rad/s
α = Angular Acceleration = ?
t = time = 5 s
Therefore,
2000 rad/s = 7000 rad/s + α(5s)
α = (2000 rad/s - 7000 rad/s)/5 s
<u>α = - 1000 rad/s²</u>
<u>Negative sign represents deceleration.</u>
(b)
Using second equation of motion:
θ = ωi t + (1/2)αt²
where,
θ = No. of Rotations = ?
Therefore,
θ = (7000 rad/s)(5 s) + (1/2)(- 1000 rad/s²)(5 s)²
θ = 35000 rad - 12500 rad
θ = (22500 rad)(1 rotation/2π rad)
<u>θ = 3581 rotations</u>
(c)
Length of String = L = (Circumference of Pulley)(θ)
L = [2π(0.08 m)][3581 rotations]
<u>L = 1800 m</u>
<u></u>
(d)
Tangential Acceleration = a = rα
a = (0.08 m)(-1000 rad/s²)
<u>a = - 80 m/s²</u>
