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These are the key concepts that have been discussed in the following Lecture Slides : Angular Momentum, Linear Momentum, system of particles, Solid Body, ExternAl Torque, Conserves Angular Momentum, Thin Disk, Rotation axis, Heavy Ostrich egg, net torque
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A particle at location r (measured from point O) moving with
momentum p = m v has an angular momentum defined as the
vector product
As in the case for linear momentum, a system of particles has a
net angular momentum given by the sum of the individual
particle contributions
i
i
p
r
O
A solid body rotating with angular velocity ω about an axis of
symmetry O has angular momentum defined by
where I is the moment of inertia
measured about the rotation axis O.
If no external torque acts on the body while internal forces cause
its moment of inertia to change, then the angular velocity will
react in a manner that conserves angular momentum
€
L = I ω
L f
= L i
I f
ω f
= I i
ω i
v
v
Torque is the time rate of change of angular momentum
momentum. In particular, a pair of colliding objects conserves the
net angular momentum, L after
before
, if Στ=0.
change its angular velocity (spin up or down).
to change the direction of its angular momentum , a phenomenon
known as precession.
€
τ ∑
=
dL
dt
Precession
2
trans
2
rot
2
nd
||
ext
ext
Two dumbbells rest on a horizontal, frictionless surface (top view
shown above). A force F is applied to each dumbbell for a short
time interval Δ t , either: (a) at the center or (b) at one end. After
the impulses are applied, how do the center-of-mass velocities of
the dumbbells compare?
motion of a system.
system’s rotation about its COM.
€
F ∑
=
dP
dt
€
τ ∑
=
dL
dt
Δ K tot
= W tot
= W trans
