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Last Lecture
Everything you need to know about dynamics of rotation
Today
Pendulums and Kinetic Energy of rotation
Important Concepts
Equations for angular motion are mostly identical to those
for linear motion with the names of the variables changed.
Kinetic energy of rotation adds a new term to the same
energy equation, it does not add a new equation.
Kinetic energy can be simply written as a linear term and
a rotational term
8.01L IAP 2007
1/16/2007
Important Reminders
Note that tutors have both assigned and open
sessions this week. See web for schedule
Mastering Physics due tomorrow at 10pm.
Experiment in class on Thursday.
Note that if you do NOT do the necessary calculations in
advance, there is a good chance that you will NOT be
able to finish the experiment in time.
Problems-solving in recitation this Friday.
Pset due this Friday at 4:30pm.
8.01L IAP 2007
1/16/2007
Right-Hand-Rule Review (by request)
Except for the gyroscope, all 8.01L problems can be
solved without using R-H-R, use CW/CCW instead.
However, many problems in 8.02 require R-H-R
The vector for any angular quantity (, , , , J)
points along the axis with the direction given by:
Fingers curl in direction of , , , , J, thumb points in the
direction of the vector
r r
Cross-product Right-Hand-Rule: A  B  C
Fingers point along vector A, curl fingers to point
along vector B, thumb points in direction C.
8.01L IAP 2007
1/16/2007
Pendulums
Simple pendulum: Small mass at the end of a string
Period is T
 2
l
g
where l is the length from the
pivot to the center of the object.
Physical pendulum: More complex object rotating
about any pivot
Period is T
 2 I
Mgl
where l is the distance from
the pivot to the center of mass of the object, M is the total
mass, and I is the moment of inertia around the pivot.
8.01L IAP 2007
1/16/2007
Parallel Axis Theorum
Very simple way to find moment of inertia for a large
number of strange axis locations.
d
c.m.
Axis 1
I1 = Ic.m. + Md2 where M is the total mass.
8.01L IAP 2007
1/16/2007
Kinetic Energy with Rotation
Adds a new term not a new equation!
Rotation around any fixed pivot: KE  12 I pivot 2
2
Moving and rotating: KE  ICM   M Tot vCM
1
2
8.01L IAP 2007
2
1
2
1/16/2007
Everything you need to know for
Linear & Rotational Dynamics
r
r
 F  Ma
r
r
   I
This is true for any fixed axis and for an axis through the
center of mass, even if the object moves or accelerates.
Rolling without slipping: v  R a  R f   N
Friction does NOT do work!
Rolling with slipping: v  R a  R f   N
Friction does work, usually negative.
Rarely solvable without using force and torque equations!
8.01L IAP 2007
1/16/2007