Transcript A Brief History of Planetary Science

PH 201
Dr. Cecilia Vogel
Lecture 20
REVIEW
Constant angular
acceleration equations
Rotational Motion
torque
OUTLINE
moment of inertia
angular momentum
angular kinetic energy
Table so Far
Linear
variable
x
v = dx/dt
a = dv/dt
F
m
K
p
Angular
variable
Variable name
q
w = dq/dt
a = dw/dt
angle (rad)
angular velocity (rad/s)
ang. acceleration (rad/s2)
torque (Nm)
moment of inertia (kgm2)
t
I
Recall Momentum
Momentum is conserved,
if no external force
because
SF=mDvCM/Dt
So if LHS=0, DvCM=0
then Dp=0
Angular Momentum
St=IDw/Dt
So if LHS =0
then IDw = 0
Define angular momentum
L = Iw
Angular momentum conserved
if no net external torque
Add to Table
Linear
variable
x
v = dx/dt
a = dv/dt
F
m
K = ½mv2
p
Angular
variable
Variable name
q
w = dq/dt
a = dw/dt
t
I
Krot = ½Iw2
angle (rad)
angular velocity (rad/s)
ang. acceleration (rad/s2)
torque (Nm)
moment of inertia (kgm2)
Rotational Kinetic Energy (J)
L=Iw
Angular momentum (kgm2/s)
Angular Momentum
St=IDw/Dt
So if net torque is not zero
then L changes
angular momentum changes
dL
St =
dt
Angular Momentum
angular momentum is a vector
direction is found by a RHR
Hold your right hand so your curved
fingers point in the direction of rotation
then your thumb will point in the direction
of angular momentum (out +, in -)
Conservation Demo
Sit on a chair, free to rotate
hold a wheel rotating so its angular
momentum points to your left.
Try to tip wheel’s axis up or down.
Notice
torque required for you to change angular
momentum of wheel (just direction).
You and wheel are isolated, so if you tip
wheel axis down,
to conserve momentum need L ___.
Demo and Bikes
Sit on a bike
wheels rotate so angular momentum
points to your left.
Lean the bike.
If you tip wheel axis down, (lean left)
to conserve momentum need L ___
Bike turns ___
Kinetic Energy of Rotation
As a rigid body rotates,
all parts are moving
but different parts are moving at different
speeds,
so
If you consider
then
K rot = Iw
1
2
2
Add to Table
Linear
Angular
Variable name
variable
variable
x
angle (rad)
q
v = dx/dt w = dq/dt angular velocity (rad/s)
a = dv/dt a = dw/dt ang. acceleration (rad/s2)
F
torque (Nm)
t
m
I
moment of inertia (kgm2)
K = ½mv2 Krot = ½Iw2 Rotational Kinetic Energy
p
Total Kinetic Energy
An object might be rotating, while also
moving linearly,
like a tire on a bike that’s being ridden.
Has
and
K = K rot  KCM
note: Krot must be rotation about CM