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Question

A particle starts from rest and moves in a circular motion with constant angular acceleration of 2 rad/s2. Find
a. Angular velocity
b. Angular displacement of the particle after 4 s
c. The number of revolutions completed by the particle during these 4 s.
d. If the radius of the circle is 10 cm, find the magnitude and direction of net acceleration of the particle at the end of 4 s.

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Solution

α=2rads2,ω1=0,t=4s
a.)ω=ω1+αtω2=0+2×4=8rads1
b.)θ=ω1t+12αt2θ=0×4+12×2×42=16rad
c.) 1 revolution =2πrad1rad=12rev16rad=162πrev=8πrev=8×722=2811rev
d.) After 4s:v=ω2r=8×10/100=0.8ms1
ac=v2r=(0.8)210/100=6.4ms2
Now magnitude of net acceleration,
a=a2c+a2t=6.42+0.22=41ms2
Direstion on acceleration
tanθ=atac=0.26.4=132θ=tan1(132)

1027141_985289_ans_b58aa91513b64e879f6cd62984cb8de0.PNG

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