× Didn't find what you were looking for? Ask a question
Top Posters
Since Sunday
5
o
5
4
m
4
b
4
x
4
a
4
l
4
t
4
S
4
m
3
s
3
New Topic  
cloveb cloveb
wrote...
Valued Member
Posts: 792
7 years ago
A pulley is accelerated uniformly from rest at a rate of 8 rad/s 2 . After 20 s the acceleration stops
 and the pulley runs at constant speed for 2 min, and then the pulley comes uniformly to rest after a further 40 s. Calculate: (a) the angular velocity after the period of acceleration,
 (b) the deceleration,
 (c) the total number of revolutions made by the pulley.
Read 211 times
1 Reply

Related Topics

Replies
wrote...
Staff Member
7 years ago
(a) Angular velocity after acceleration period,ω2 = ω1+ αt = 0 + (8)(20) = 160 rad/s

(b) ω3 = ω2 + αt from which,

angular acceleration, α = (ω3 - ω2)/t = (0 - 160)/40 = - 4 rad/s2

i.e. angular deceleration is 4 rad/s2

(c) Initial angle turned through, θ1 = [(ω1 + ω2)/2]*t = [(0 + 160)/2]*(20) = 1600 rad =1600/2π rev

 At constant speed, angle turned through, θ2 = 160 rad/s × (2 × 60)s = 19200 rad = 19200/2π rev

Angle turned through during deceleration, θ3 = [(160+ 0)/2]*(40) = 3200 rad = 3200/2π rev

Hence, total number of revolutions made by the pulley = θ1+ θ2 + θ3

=1600/2π +19200/2π + 3200/2π

=24000/2π = 12000/π rev or 3820 rev
New Topic      
Explore
Post your homework questions and get free online help from our incredible volunteers
  901 People Browsing
 113 Signed Up Today
Related Images
  
 593
  
 1032
  
 248
Your Opinion
Which industry do you think artificial intelligence (AI) will impact the most?
Votes: 308