Physics Department
PHYS 1P21/1P91
Outline
Textbook
Homework
Introduction
Kinematics
Dynamics
Rotational Motion
Work, energy and Momentum
Oscillations and Waves
Formula Sheet
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RotationalMotion
Mechanics and Waves
Introduction
Kinematics: motion in one and two dimensions
Dynamics
Rotational motion
Torque
A second condition is necessary for
static equilibrium
torque
is the turning effect of a force
MC:
rank these torques I
MC:
rank these torques II
Static Equilibrium
MC:
teeter-totter
center of mass
do you know where your
center of gravity
is?(
oops
)
locating the
center of gravity
MC:
two-particle system
Ex:
a many particle system
Ex:
symmetric sawhorses
Ex:
asymmetric sawhorses
Ex:
a diving board
Ex:
the sign problem
Ex:
the ladder problem with no wall friction
Ex:
the ladder problem including wall friction
Stable, Unstable and neutral
equilibrium
Rotational Kinematics
Review: circular motion of point particles
uniform circular motion
defined
definitions:
angular position, frequency, period
angular
velocity
and
tangential velocity and centripetal acceleration
MC:
compare the tangential velocities
Direction of
centripetal acceleration
non-uniform circular motion:
a
=
a
t
+
a
c
(
a model plane
,
a discus thrower
)
angular acceleration and tangential acceleration
rigid body rotation
angular displacement
MC:
positive and negative displacements
Angular velocity
Ex:
a watch
vector nature of the angular velocity:
right-hand-rule
convention
MC:
a barrel
Angular acceleration
relative sign of angular velocity and
acceleration
Every particle in rigid body shares same ω and α but
v
t
, a
t
and a
c
depend on radius
Rotational Kinematic Equations
rotational kinematic equations
are analogous to the linear equations
Ex:
a fan changing speeds
Ex:
record player
Sapling problem: Definitions of
angular quantities
Rotational Dynamics
Moment of Inertia
Rotational Kinetic Energy
and the definition of moment of inertia
MC:
inertia depends on mass distribution
moment of inertia depends on
mass distribution
MC:
moment of inertia depends on the axis of rotation I
MC:
moment of inertia depends on the axis of rotation II
Ex:
calculating rotational KE
MC:
compare the rotational KE
N2L for rotations
an industrial flywheel
Ex:
flywheels
Problems with fixed axis of rotation
Ex:
Atwood machine revisited
Ex:
A dual-pulley
Rolling motion
v
CM
=v
T
a rolling tire
total velocity:
a bike wheel
In a
rolling object
,
v
CM
=v
T
Ex:
an accelerating car
Ex:
Compare the
the total kinetic energy
MC:
a race between balls
Angular Momentum
definition of angular momentum
angular momentum of
point particles
-->
angular momentum of extended objects
Ex:
a rolling log
Conservation of angular momentum
Figure Skating World Record
Merry Go Round of Death
MC:
how does the
angular velocity change?
Ex:
collapsing star
MC:
global warming
Ex:
playground merry-go-round
Rotational "collision" (1:15-1:25)
Gyroscope
Rolling motion
v
CM
=v
T
a rolling tire
total velocity:
a bike wheel
Ex:
an accelerating car
Rotational Dynamics
N2L for rotations
Ex:
comparing moments of inertia
Ex:
moment of inertia depends on the axis of rotation I
Ex:
moment of inertia depends on the axis of rotation II
Ex:
inertia depends on mass distribution
Ex:
Atwood machine revisited
Ex:
A dual-pulley
Work, energy, momentum
Oscillations and waves
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Updated: 13-Jan-2021 11:53