SPECIAL OFFICE HOURS:
Tuesday: 11AM-1PM
Uniform circular motion is due to a centripetal acceleration
This acceleration is always pointing to the center
This acceleration is due to a net force
arad = v2/R
A diagram of gravitational force
We want to
place a
satellite into
circular orbit
300km
above the
earth
surface.
What speed,
period and
radial
acceleration
it must
have?
What is “work” as defined in Physics?
•Formally, work is the product of a constant force F
through a parallel displacement s.
W is N.m
W = F.s
1 Joule (J) = (1N.m)
W>0
W<0
W=0
Work and Kinetic Energy
work-energy theorem
W = Kf - Ki
Gravitational Potential Energy (Near Earth’s
surface)
U = mgy
Uel = (1/2) kx2
• Work-Energy Theorem
Wtotal = Kf – Ki
• Conservatives force
Kf + Uf = Ki + Ui
• Non-conservative forces
Kf + Uf = Ki + Ui + Wother
Off center collisions
Suppose we have several particles A, B, etc., with masses
mA, mB, …. Let the coordinates of A be (xA, yA), let those
of B be (xB, yB), and so on. We define the center of
mass of the system as the point having coordinates
(xcm,ycm) given by
xcm = (mAxA + mBxB + ……….)/(mA + mB + ………),
Ycm = (mAyA + mByB +……….)/(mA + mB + ………).
v = rω
atan = rα
arad = rω2
2
2
a  atan
 arad
Kinetic Energy of Rotating Rigid Body
Moment of Inertia
KA = (1/2)mAvA2
vA = rA ω
vA2 = rA2 ω2
KA = (1/2)(mArA2)ω2
KB = (1/2)(mBrB2)ω2
KC = (1/2)(mCrC2)ω2
..
K = KA + KB + KC + KD ….
K = (1/2)(mArA2)ω2 + (1/2)(mBrB2)ω2 …..
K = (1/2)[(mArA2) + (mBrB2)+ …] ω2
K = (1/2) I ω2
I = mArA2 + mBrB2 + mCrC2) + mDrD2 + …
Unit: kg.m2
Rotation about a Moving Axis
• Every motion of of a rigid body can be represented
as a combination of motion of the center of mass
(translation) and rotation about an axis through the
center of mass
• The total kinetic energy can always be represented as
the sum of a part associated with motion of the center of
mass (treated as a point) plus a part asociated with
rotation about an axis through the center of mass
Total Kinetic Energy
Ktotal = (1/2)Mvcm2 + (1/2)Icmω2
Rotation about a moving axis
Conservation of angular momentum
When the sum of the torques of all external
forces acting on a system is zero, then
THE TOTAL ANGULAR MOMENTUM
IS CONSTANT (CONSERVED)
The professor as figure skater?
•It seems that danger to the instructor is proportional to interest in
any given demonstration.