Download - Rotation, angular motion & angular momentom
Rotation, angular motion & angular momentom
Physics 100
Chapt 6
Rotation
Rotation
d1
d2
The ants moved differentdistances: d1 is less than d2
Rotation
Both ants moved theSame angle: 1 = 2 (=)
Angle is a simpler quantity than distance for describing rotational motion
Angular vs “linear” quantities
Linear quantity symb. Angular quantity symb.
distance d angle velocity v
change in delapsed time=
angular vel.
change in elapsed time=
Angular vs “linear” quantities
Linear quantity symb. Angular quantity symb.
distance d angle
acceleration a
change in velapsed time=
angular accel.
change in elapsed time=
velocity v angular vel.
Angular vs “linear” quantities
Linear quantity symb. Angular quantity symb.
distance d angle
acceleration a angular accel. velocity v angular vel.
Moment of inertia = mass x (moment-arm)2
mass m
resistance to change in the state of (linear) motion
Moment of Inertia I (= mr2)
resistance to change in the state of angular motion
M
x
momentarm
Moment of inertial
M Mx
r r
I Mr2
r = dist from axis of rotationI=small
I=large(same M)
easy to turnharder to turn
Moment of inertia
Angular vs “linear” quantities
Linear quantity symb. Angular quantity symb.
distance d angle
acceleration a angular accel. velocity v angular vel.
Force F (=ma) torque (=I)
torque = force x moment-arm
Same force;bigger torque
Same force;even bigger torque
mass m moment of inertia I
Teeter-Totter
F
Fbut Boy’s moment-arm is larger..
His weight produces a
larger torque
Forces are the same..
Angular vs “linear” quantities
Linear quantity symb. Angular quantity symb.
distance d angle
acceleration a angular accel. velocity v angular vel.
Force F (=ma) torque (=I)
mass m moment of inertia I
momentum p (=mv) angular mom. L(=I)
Angular momentumis conserved:
L=const
I = I
Conservation of angular momentum
I
I
I
High Diver
I
I
I
Conservation of angular momentum
II
Angular momentum is a vector
Right-hand rule
Conservation of angular momentum
L has no verticalcomponent
No torques possible Around vertical axisvertical component of L= const
Girl spins:net vertical
component of Lstill = 0
Turning bicycle
L
L
These compensate
Torque is also a vector
wrist bypivot pointFingers in
F direction
F
Thumb in
direction
another
right-hand ruleF
pivotpoint
is out ofthe
screen
example:
Spinning wheel
F
wheel precesses
away from viewer
Angular vs “linear” quantities
Linear quantity symb. Angular quantity symb.
distance d angle
acceleration a angular accel. velocity v angular vel.
Force F (=ma) torque (=I)
mass m moment of inertia I
momentum p (=mv)
kinetic energy ½ mv2
angular mom. L(=I)
rotational k.e. ½ I
I
V KEtot = ½ mV2 + ½ I2
Hoop disk sphere race
Hoop disk sphere race
I
I
I
Hoop disk sphere race
II
I
KE = ½ mv2 + ½ I2
KE = ½ mv2 + ½ I2
KE = ½ mv2 + ½ I2
Hoop disk sphere race
Every sphere beats every disk
& every disk beats every hoop