1	Chapter 4 Rotary Motion
2	Types or Names for Rotary Motion Rotating Circling Revolving Spinning Twisting Pirouetting Turning Somersaulting
3	Rotation within the Body – Axis is in the joint Joints can act like hinges in the case of the elbow and knee, and have one axis of motion. Some are ball and socket joints like the hip and shoulder, and have three axes of rotation. Some joints are pivot joints like the proximal radioulnar joint, and the atlanto-dental joint, and one axis of rotation Some are condyloid joints with two axes of rotation, like the wrist and finger joints.
4	Rotation within the body while airborne – Axis is CG Diving; twisting, somersaulting Pole vaulting when release from pole High jumping
5	Rotation within the body while holding an implement – Axis is distal joint or line through body Golf club rotation around an axis in the body; multiple joint motions, including the wrist Baseball bat rotation using multiple joints
6	Rotation can be outside the body – Axis of Rotation is outside the body Around the curved track Swinging from a high bar, rings, or parallel bar Figure skating Front or back handsprings, cartwheels in Tumbling
7	Rotation applied to an object – Axis or rotation is in the object Spin put on a ball, like a baseball curve Boomerang throw Frisby throw Football field goal or kick off
8	Angular Motion Pure angular motion means that all points on an object go through the same angle. Angles are measured in degrees, radians, or revolutions Angular motion must have an axis of rotation about which the object turns
9	Lever Systems The body has been called a “system of levers” A lever is a simple machine that transmits and changes mechanical energy from one place to another. The muscles, bones, and joints act in a leverage type system. Force is applied to one location of a lever, and resistance applies a force to another. The Force applied to the lever makes it rotate around a fulcrum.
10	Figure 4.2:Components of a Lever
11	Figure 4.3
12	Figure 4.4
13	Torque Torque is a turning effect related to the force acting on the lever and the length of the lever. The biceps muscle applies a force to the lever and acts at a perpendicular distance from the axis of rotation, the elbow joint. It produces a torque to raise the dumbbell The dumbbell produces a resistance torque based on the weight and the perpendicular distance to the axis of rotation, the elbow.
14	Figure 4.5
15	Torque Torque is equivalent to the product of the Force times the perpendicular distance from the action line of the force to the axis of rotation.
16	Figure 4.13
17	Figure 4.6
18	Types of Levers First Class: Effort – Fulcrum – Resistance (EFR) Second Class: Fulcrum – Resistance – Effort (FRE) Third Class: Fulcrum – Effort – Resistance (FER)
19	First Class Lever EFR – Effort-Fulcrum-Resistance Triceps in Elbow Extension
20	Second Class Lever FRE – Fulcrum – Resistance – Effort Wheelbarrow
21	Second Class Lever
22	Third Class Lever Fulcrum – Effort – Resistance
23	Third Class Lever
24	Advantages and Disadvantages of the Levers In a second class lever, FRE, where the Resistance is closer to the fulcrum than the Effort; or the Effort Arm is longer than the Resistance Arm: Advantage: With less Effort one can move a Resistance much greater than the Effort put into it. Disadvantage: The Effort must move through a range of motion much greater than the Resistance.
25
26	"In a Third Class lever" In a Third Class lever, FER, where the Resistance Arm is much greater than the Effort Arm: Advantage: Can move the resistance through a greater range of motion, and at a higher velocity than the effort. Disadvantage: It usually requires much more effort than the resistance itself.
27	Figure 4-13
28	Figure 4-15
29	Initiation of Rotation ANYTIME AN ATHLETE APPLIES FORCE AT A DISTANCE FROM THE AXIS OF ROTATION THERE IS PRODUCED A TURNING EFFECT. INCREASING EITHER THE DISTANCE OR THE FORCE INCREASES THE TURNING EFFECT EXAMPLES: TENNIS SPIN, VB SPIN, NO SPIN FLOATERS THE FORCE IS DIRECTED THROUGH THE CG.
30	Figure 4-18
31	Application of Top Spin and Back Spin
32	Figure 4-20
33	Figure 4-21
34	Figure 4-22
35	Figure 4-24
36	Centrifugal Force Anytime there is a mass rotating around an axis that is not through the CG, there is centrifugal force. Example: Hammer throw Centrifugal vs. Centripetal Centripetal means “center seeking”, and centrifugal is pulling away from the center of the arc. Remember the law of “action-reaction”
37	"F_c" F_c = mw² r = mV² /r Remember that the linear V of the object on the arc is the angular velocity (radians) times the radius: wr = V When the thrower releases his grip on the hammer, it will go in a straight line at velocity V.
38	Figure 4-25
39	"We can replace wr" We can replace wr for V in mV² /r F_c = m (wr ) ² / r = m w²r² / r = mw² r Examples in sport: Speed skater going into a turn; 200m sprinter going into a turn. Inertia wants to continue in a straight line In order to change direction, one needs a force that will prevent the body from continuing to go straight.
40	Rotary Inertia Rotary Resistance It is the resistance to being rotated. Rotary persistance means that an object that is spinning will continue to spin unless slowed down by an outside torque; like friction, air resistance.
41	Newton’s First Law Applied to Rotation An object that is spinning will continue to spin at a constant angular velocity until acted upon by an unbalanced torque. Linear: mass is inertia Angular: Moment of inertia (I) is the distribution of mass about the axis of rotation.
42	Moment of Inertia Moment of Inertia is: I = Σ mr²
43	Moment of Inertia of Baseball Bat
44
45	Moment of Inertia of the Human Body in Layout, and Pike Positions
46	Moment of Inertia of the Human Body in Tuck Position and Swinging
47	Rotary Inertia in Sprinting The sprinter flexes the knee of the push off leg in order to reduce the moment of inertia of the leg. With a smaller moment of inertia it is much easier to get the leg forward, and the leg moves much faster than if it were straight.
48
49	Angular Momentum Like linear momentum, mV, angular momentum is Iω Notice that rotary inertia, I, is analogous to mass, and angular velocity, ω, is analogous to linear velocity, V. As an object is spinning, it has a certain amount of angular momentum based on its moment of inertia and its angular velocity, Iω
50	Linear and Angular Momentum In order to increase the velocity of an object we need to apply a force. F = (mV_f – mV_i) / t Likewise, in order to increase the angular velocity of an object we need to apply a Torque. T = (Iω_f - Iω_i) / t Notice that Force is analogous to Torque
51	"The baseball bat can be..." The baseball bat can be made heavier, or longer If longer with the same mass, the rotary inertia will increase; If heavier with the same length, the I will increase. As the moment of inertia increases it is harder to swing the bat. The angular velocity of the bat becomes less.
52	Newton’s Second Law Applied to Rotation Linear: F = ma Angular: T = Iα In order to get an object rotating it takes a torque; that is, change the angular velocity of the object. T = I (ω_f – ω_i )/ t = (I ω_f – I ω_i )/ t I ω is angular momentum In order to change the angular momentum in time, t, it takes a torque
53	Components of Angular Momentum, H Mass How the mass is distributed relative to the axis of rotation, about which the object is spinning. The rate of rotation, or swing (angular velocity) When bats and clubs are swung there is a trade-off between the mass , its length, and the distribution of the mass around the axis of rotation, and the rate of rotation.
54	"In baseball," In baseball, there has been no batter who has used a 42in bat. The legal limit. Players usually use a bat between 32 and 34 oz. although there is no legal limit. The heavier the bat, or the greater the rotary inertia, I, of the bat the slower is the swing, the longer it takes to accelerate, α, the bat. A pitch only gives the batter about 0.54 seconds from the time of release until it crosses the plate.
55
56	Increasing Angular Momentum Can be increased in three ways: 1) Increase the mass of whatever is rotated. 2) Shift as much of the mass as far from the axis of rotation as possible. 3) Increase the angular velocity of whatever is rotating
57	Increasing angular velocity To change angular velocity of an object it takes a torque. If the batter has a bat with greater rotary inertia, it will take more torque to increase the angular velocity the same amount as the lighter bat. If the batter was using maximum torque on the lighter bat, the heavier bat will only accelerate (α ) less, taking more time to cross the plate
58	Conserving Angular Momentum Conserve means stay constant, or the same. Angular momentum is generated from the push-off of the high jump, long jump, diving, etc. It is generated by the push-off force NOT directed through the CG. Once the athlete leaves the ground, the angular momentum is fixed and cannot be changed no matter what the athlete does in the air.
59
60	Changing Moment of Inertia in the Air Although the athlete cannot change Angular Momentum in the air, the athlete can change Moment of Inertia, I, about the CG. The CG is the axis of rotation Example: Layout Dive
61	Moment of inertia about the CG in the Pike, and Tuck Dives
62	Moment of Inertia about an axis other than the CG
63	Control of the Rate of Spin in Diving By changing the body configuration from layout to pike or tuck, the athlete is changing his moment of inertia around his CG The diver pulls his mass closer to the axis of rotation, reducing all the little mr² s. Since the Angular Momentum cannot change and I has been reduced, ω must increase
64	Conservation of Angular Momentum
65	Increasing rate of spin Other sports which use the reduction of moment of inertia to increase rate of spin is demonstrated in figure skating. The skater makes a circle on the ice and reduces the radius of the circle until it is very small or a point. The H developed going into the circle is maintain nearly the same, but as the circle is reduced, and the arms are pulled in, the skater spins faster and faster, especially when they are spinning on a point.
66	"The skater leaps into the..." The skater leaps into the air with one leg forward and the other back. There is a certain spin present from take-off. Then the skater pulls the legs and arms in tight and the skater spins along the long axis of the body. Remember the angular momentum is around an axis, the bilateral axis in the layout, pike, and tuck dives, the longitudinal axis for the skater.
67	Changing body position in the air When the athlete changes body position in the air by moving one body part, another body part must move also. This is action-reaction in the angular sense. As the diver pulls the legs up into a pike, the trunk must go forward to compensate for the change in the position of the legs. If one thinks of the CG as the axis of rotation, then the movement of the legs in one direction would cause a change in the angular momentum, unless there was an equal and opposite movement of the upper body toward the legs.
68
69	Path of CG during airborne activities cannot be changed Once the athlete leaves the ground the path of the CG is fixed and cannot be changed. In the layout position, the CG of the diver is inside the body, however in the pike position it is outside the body.
70	"As the diver moves from..." As the diver moves from the layout to the pike, the CG moves outside the body, and the hips and pelvis move backward.
71	High Jumper When the high jumper arches over the bar with the hips up and the head and legs down, the jumper will need to clear the legs after the hips clear. When the legs are raised the trunk moves up also to compensate for the change in angular momentum of the legs. This is an equal and opposite reaction.
72
73	Volleyball Spiker When the spiker in VB brings her arm forward to strike the ball, the change in H of the upper body must be compensated by an equal and opposite change in H of the lower body. Thus the lower body comes forward and upward to compensate for the forward and downward movement of the arms and trunk.
74	Transferring Angular Momentum to Other Axes of Rotation Divers, trampolinists, and ski-aerialists can combing somersaults and twists. Somersaults are around the bilateral axis through the CG, while twists are around the longitudinal axis.
75