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.

Principle 7: 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 Sometimes athletes need to generate as much angular momentum as possible; on other occasions they need to minimize it. In sport it is important for athletes to control angular momentum. 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.

Application 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.