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Unformatted text preview: TYPES OF MOTION OF A RIGID BODY By deﬁnition a rigid body consists of many mass points (mi) located at different points (r, ) but (r, — 13. ) is ﬁxed so it neither changes shape nor size as it moves. This 151in considbrable
simpliﬁcation in describing the two types of motion it can have: _ _ For a rigid body one can deﬁne a center of gravity and show that it is the same as the center of V
mass. Zmi 7";
rem : —' ._., 2m! Consider a rigid body placed some distance above the Earth. i) Each mass m experiences a force Total force on rigid body w = 2W, = ~Emig3") n as if it was a single object of mass M. ii) Each mass m has potential energy Pg (0 : mg)»,
Total potential energy Pg =zmigyi :ngcm Emigi
2m 1 As if it was a single mass M located at the center ofrnass of the rigid body; Since ycm : TWTESOFRMIHON Translation: All the masses have the same linear velocity and the same linear acceleration
“ 2E¢O
21' = A
J. V :: V X
a [Indeed y = vC,G ] ._.____, ) Rotation about a ﬁxed axis: Now the angular velocity and the angular acceleration are the same
for all m ' Now 2F. : 0 For equilibrium we need two conditidns
g=0 and g=0 so 2F, 50 27,50 All torques taken about a single axis. The table below summarizes the equations when 9! i 0 and g at 0. (Dynamics) Translation (one dimension, x) ' Rotation (Fixed axis, Z)
§ 9
g Q.
g=a“ g:a",a,=ar,f* —> .R:
I] (v, + 6109? Q : (mi + 0502, v, = com" * A 1 A
2g=(x. +v.t+%at2)x @=(®, +w,r+§at2)z v2 =v,2+2a2(x—x,) w2=wi2+2a2(®—®i‘)
Displacement along c
AS .= PA®
M (M333) I = EM”;2 (Moment of Inertia)**
M g 2 BF, I Q; = 21',
At that point About same axis as I
At that time **1 measures the manner in which the mass is
distributed around the axis so 27, must also be calculated using the same axis. ...
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 Spring '10
 Shawhan
 Physics

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