Pendulums
Important Reminders
Last Lecture
Everything you need to know about dynamics of rotation
Contact your tutor about session scheduling
Today
Simple pendulum: Small mass at the end of a string
Mastering Physics due tomorrow at 10pm.
Pendulums and Kinetic Energy of rotation
Period is
Pset due this Friday at 11am.
Important Concepts
Equations for angular motion are mostly identical to those
for linear motion with the names of the variables changed.
Period is T
Kinetic energy can be simply written as a linear term and
a rotational term
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c.m.
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= 2!
I
Mgl
where l is the distance from
8.01L IAP 2006
1/17/2006
Everything you need to know for
Linear & Rotational Dynamics
Adds a new term not a new equation!
!
!
 !F = Ma
Rotation around any fixed pivot: KE = 12 I pivot! 2
 !" = I#
!
2
1
2
!
This is true for any fixed axis and for an axis through the
center of mass, even if the object moves or accelerates.
Moving and rotating: KE = I CM ! + M v
1
2
Axis 1
where l is the length from the
mass, and I is the moment of inertia around the pivot.
8.01L IAP 2006
Kinetic Energy with Rotation
d
g
the pivot to the center of mass of the object, M is the total
Parallel Axis Theorum
Very simple way to find moment of inertia for a large
number of strange axis locations.
l
Physical pendulum: More complex object rotating
about any pivot
Kinetic energy of rotation adds a new term to the same
energy equation, it does not add a new equation.
8.01L IAP 2006
T = 2!
pivot to the center of the object.
2
Tot CM
Rolling without slipping: v = R! a = R" f # µ N
Friction does NOT do work!
Rolling with slipping: v ! R" a ! R# f = µ N
I1 = Ic.m. + Md2 where M is the total mass.
Friction does work, usually negative.
Rarely solvable without using force and torque equations!
8.01L IAP 2006
1/17/2006
8.01L IAP 2006
1/17/2006
8.01L IAP 2006
1/17/2006
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