2D rigid body dynamics  Work and power for rotational motion
,
()
/
ave
W
Pt
P
τθ
τω
=
⋅
=
⋅Δ
=
⋅
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
2D rigid body dynamics – Energy equation including the rotational motion
111
1
2
2 22
ge
g
KU U W KU U
−
e
′
+++
=
++
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
12
k
WN
s
μ
−
′
=
−+
⋅
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
θ
up from the horizontal direction. Find the angular velocity of the rod whenit swings down to the vertical position.
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 Fall '08
 TSChang
 Physics, Energy, Kinetic Energy, Mass, Potential Energy, Power, Work, Rigid Body Dynamics

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