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2D Rigid Body Rotational Kinetics – Work, Power, and Energy equation
−
Work and power for rotational motion
,
for constant torqu
e
W
P
τ
θ
τ ω
=
⋅Δ
=
⋅
is the angle of rotation or angular displacement
(
)/
ave
W
d
P
t
τ
θ
τ
θ
θ
=
⋅
=
⋅Δ
Δ
Δ
∫
e
Example
A disk with mass 15 Kg and radius 0.4 m is pivoted at its center. A constant torque of 30 Nm supplied by a motor
turns the disk from rest. (a) Calculate the work produced by the motor from
t
= 0 to
t
= 8 s. (b) Find the average
power provided by the motor from
t
= 0 to
t
= 8 s. (c) Find the instantaneous power output of the motor at
t
= 8 s.
Ans
: (a) 24 kJ (b) 3 kW (c) 6 kW
– Energy equation including the rotational motion
1
1
1
1 2
2
2
2
g
e
g
K
U
U
W
K
U
U
−
′
+
+
+
=
+
+
Rotational kinetic energy
K
= (1/2)
I
ω
2
Translational kinetic energy
K
= (1/2)
m
υ
2
Gravitational potential energy
U
g
=
mgy
cm
Elastic potential energy
U
e
= (1/2)
kx
2
1 2
k
W
N s
μ
τ θ
−
′
= −
+
⋅
Example
1. The slender rod of mass
m
and length
L
is pivoted at point
O
, and it is released from rest as shown at an angle
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 Spring '08
 TSChang
 Physics, Energy, Kinetic Energy, Mass, Potential Energy, Power, Work, Δθ, constant torque, Body Rotational Kinetics

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