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hichkok12
1 month ago
11

A pulley of radius 8.0 cm is connected to a motor that rotates at a rate 7000 rad s-1 and then decelerate uniformly at a rate of

2000 rad s-1 within 5 s.
a. Calculate its angular acceleration.
b. What is the number of rotations within the time range?
c. How long is the string that winds it within the time range?
d. Determine the tangential acceleration of the string.
[15 marks]​
Physics
1 answer:
Maru [3.3K]1 month ago
4 0

Answer:

(a) α = - 1000 rad/s²

The negative indicates deceleration.

(b) θ = 3581 rotations

(c) L = 1800 m

(d) a = - 80 m/s²  

Explanation:

(a)

Using the 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

Hence,

2000 rad/s = 7000 rad/s + α(5s)

α = (2000 rad/s - 7000 rad/s)/5 s

α = - 1000 rad/s²

The negative denotes deceleration.

(b)

Applying the second equation of motion:

θ = ωi t + (1/2)αt²

where,

θ = Number 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)

θ = 3581 rotations

(c)

The length of the string = L = (Circumference of Pulley)(θ)

L = [2π(0.08 m)][3581 rotations]

L = 1800 m

(d)

Tangential Acceleration = a = rα

a = (0.08 m)(-1000 rad/s²)

a = - 80 m/s²[[TAG_145]][[TAG_146]][[TAG_147]]
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