A particle moves in a circle with the constant speed of 10m/s. Radius of circle is 1m. Determine its angular speed after 5seconds, the covered distance, the linear and angular displacement after 5seconds, and centripetal acceleration.
Answers
Answered by
2
Answer:
Given,
Radius, r=1m
Initial angular velocity,ω
o
=12rad/s
Final angular velocity, ω=
60
2π
(
π
480
)=16 rad/s
Apply angular kinematic equation.
ω=ω
o
+αt
(a) Angular acceleration, α=
t
ω−ω
o
=
2
16−12
= 2 rad/s
2
(b) Tangential velocity, V
tangential
=ωr=r(ω
o
+αt)=12+2t
(c) Centripetal acceleration a
c
=rω
2
Net acceleration, a
net
=
rω
2
+αr
=
r(ω
o
+αt)
2
+αr
At,(t=0.5sec), a
net
=
1(12+2×0.5)
2
+2×1
=13.07ms
−2
At,(t=3sec), a
net
=
1(12+2×3)
2
+2×1
=18.05ms
−2
(d) Angular displacement at (t=3sec) , θ=ω
o
t+
2
1
αt
2
=12×3+
2
1
×2×3
2
=45rad
Similar questions