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2D Rigid body kinematics – Rotation about a fixed pivot
I. General rotation
21
Angular position:
in radians
average angular velocity
Angular velocity:
instantaneous angular velocity
average angular acceleration
Angular acceleration
:
ave
ave
tt
t
d
dt
θ
θθ
ω
α
−
Δ
==
⎧
⎪
⎪
⎨
⎪
⎪
⎩
Δ−
=
Δ
=
Δ
2
2
instantaneous angular acceleration
t
dd
dt
dt
⎧
⎪
⎪
⎨
−
=
−
⎪
⎪
⎩
II. Rotation with constant angular acceleration
0
2
00
22
1
2
2(
)
t
ωω α
θω
ωα
=
⎧
+
=+ +
=+
−
⎪
⎪
⎨
⎪
⎪
⎩
Example
A rotating wheel has an angular velocity of 10 rad/s at
t
= 0. The wheel starts to accelerate with a constant angular
acceleration of 6 rad/s
2
for 5 s, and then slows down with a constant deceleration. The wheel rotates through a total
angle of 325 rad from
t
= 0 to the time it stops. Find the angular deceleration of the wheel and total time of rotation.
Ans
: –4 rad/s
2
, 15 s
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View Full DocumentIII.
Relating rotation of rigid body and translation at a point on the body – Relating angular
motion of rigid body and linear motion of a point on the body
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 Spring '08
 TSChang
 Physics

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