Download Conservation of angular momentum

CONSERVATION OF ANGULAR
MOMENTUM
Principle 7
NOTE
• Please only copy information from slides with an * beside title.
• All other information in this presentation is important and testable!
LEARNING GOALS
• We are learning to describe angular momentum.
• We are learning to apply angular momentum to sport specific activities.
*ANGULAR MOMENTUM
Angular momentum measures the amount of angular motion that an
athlete or an object has.
• Angular momentum = Moment of Inertia x Angular velocity
• Angular momentum is fixed once the body or object is free. Only an
outside force can change it.
Principle 7: Angular Momentum
Angular momentum is constant when an athlete or object is free
in the air.
*ANGULAR VELOCITY
Angular velocity describes the rate of spin of an athlete, body
segment or object in angular motion.
Angular velocity is defined as the rate of
change of angular displacement.
*MOMENT OF INERTIA
An object or body’s resistance to change in its rate of angular
rotation.
The resistance to angular rotation.
The farther a body’s distribution of mass from the axis of
rotation, the greater its moment of inertia.
*ANGULAR MOMENTUM
• All momentum must be generated before take-off or release.
• How does a diver, gymnast, figure skater do this?
• Once free, the body can alter shape to change moment of inertia but that only
changes angular velocity.
CONTROLLING ANGULAR MOMENTUM
In sport it is important for athletes to
control angular momentum.
Sometimes athletes need to generate as much
angular momentum as possible; on other
occasions they need to minimize it.
In a dive with numerous twists or somersaults, it is
important that the diver generate both linear and
angular momentum at takeoff.
CONTROLLING ANGULAR MOMENTUM
Where does the diver use linear motion?
To get high and far enough from the platform
to be safe.
At the same time she initiates rotation. How does she
do this??
She leans forward beyond her centre of mass. The
diver can use this angular momentum to help
perform all of the somersaults and twists that occur
later in the dive.
CONTROLLING THE RATE OF SPIN
When a diver accelerates down from the 10m
tower it takes her less than two seconds to hit
the water. In flight, the diver’s angular momentum
remains constant. Her angular momentum is
determined by her rate of spin, her mass, and the
distribution of her mass.
What causes the diver to spin faster?
She tucks and pulls her mass inward (increasing her
rotary inertia). The other components of angular
momentum must increase to keep the total amount
of angular momentum unchanged.
CONTROLLING THE RATE OF SPIN
When a diver accelerates down from the 10m
tower it takes her less than two seconds to hit
the water. In flight, the diver’s angular momentum
remains constant. Her angular momentum is
determined by her rate of spin, her mass, and the
distribution of her mass.
Where does the extra angular velocity come from?
Since the diver cannot change her mass while in
flight it means that her angular velocity must
increase.
CONTROLLING THE RATE OF SPIN
What causes the skater to spin faster?
As the skater “drives” into the Axel his arms are spread out
increasing his rotary inertia. In flight the skater pulls his arms and
legs in, reducing his rotary inertia giving him more angular
velocity. The more spins that he wants to complete, the tighter
he pulls his arms into his body.
CONTROLLING THE RATE OF SPIN
What causes the skater do to slow down?
To slow down when he lands, he spreads his arms and legs out
and again his rotary inertia is increased and the rate of spin is
decreased.
TRANSFERRING MOMENTUM FROM
SOMERSAULTS TO TWISTS
Divers, gymnasts and aerial skiers often change
their axis of rotation in the air. They somersault
around their transverse axis (hip to hip) and then
twist around their long axis (feet to head).
In order to do this the diver must create tilt using the
action-reaction technique. Tilt is created by moving
the arms quickly through the plane (causing the body
to move opposite)
This tilt moves the body from the transverse (somersault)
axis toward the long (twist) axis.
TRANSFERRING MOMENTUM FROM
SOMERSAULTS TO TWISTS
After her tucked somersault the diver “kicks” out
her legs slowing down her angular momentum
The somersaulting angular momentum is then traded for
twisting angular momentum and the diver starts to twist.
When the required number of twists are
completed, the diver again changes the position
of her arms creating tilt in a different direction,
and enters the pool.
*SUMMARY
• When I move my arms out during a spin I am increasing the moment of inertia
(increasing the reluctance to spin), therefore decreasing my angular velocity.
• When I move my arms in during a spin, I am decreasing the moment of inertia
(decreasing the reluctance to spin), therefore increasing my angular velocity
(deg./time).
OTHER FORCES
INERTIA, CENTRIPETAL AND CENTRIFUGAL
FORCES
When an object is moving its inertia
wants it to travel in a straight line.
Newton’s Law of Action and Reaction also
applies to anything that rotates.
Whenever an object rotates there is
always an interplay between inertia,
centripetal force and centrifugal force.
(You cannot have one without the
others.)
Changing straight-line motion into
curved or circular motion requires a
centripetal force.
INERTIA, CENTRIPETAL AND CENTRIFUGAL
FORCES
Centripetal force pulls towards the axis of
rotation.
The inward pull of centripetal force produces
an outward pull of centrifugal force by the
hammer.
The faster the hammer swings the more
centrifugal force (b) it creates.
To compensate, the athlete must pull
harder toward the axis of rotation (a)
creating a balanced centripetal force.
APPLIC ATION
Why do the snow
boarder, downhill
skier and speed
skater lean into their
turns?
LEARNING GOALS
• We are learning to describe angular momentum.
• We are learning to apply angular momentum to sport specific activities.