Angular Kinetics

moment of inertia of angular motion depends on amount of mass, but also depends on

-also depends on additional factor=*the distribution of mass with respect to the axis of rotation*

what impact does a batter choking up have on the moment of inertia? why?

-batter choking up=reduces the moment of inertia I=mr^2 decreases r, decreases I lower inertia=easier to swing

what does not affect linear momentum that affects angular momentum?

-distribution of mass in a system DOES NOT affect linear, but does impact angular

if you hold the baseball bat by the barrel, what happens in regards to ease of swing?

-swinging the baseball bat while holding the barrel=much easier vs holding the regular handle -gripping the barrel-more mass closer to the axis of rotation, easier to swing. the radius of rotation is shorter so I ends up being smaller in the equation

how does the distribution of mass impact the moment of inertia for angular objects?

-the more closely concentrated the mass is to the AOR, the *easier* it is to swing the object because there is less resistance -the further away the concentrated mass is from the AOR, the *harder* it is to swing the object because there is more resistance

radius of gyration

:distance form the axis of rotation to a point where the body's mass could be concentrated without altering its rotational characteristics

According to Newton's 2nd Law, what is the relationship among torque, moment of inertia, and angular acceleration? A. T = Iα B. I = Tα C. α = TI D. T = Iω

A

Centripetal force is related to which of the following? A. radial acceleration B. tangential acceleration C. both A and B D. none of the above

A

If total body angular momentum is 0, what will happen as the result of a forceful movement such as a spike? A. compensatory rotation in lower body in opposite direction B. compensatory rotation in upper body called follow-through C. angular momentum is no longer 0 D. all of the above

A

Regarding moment of inertia of the leg with respect to the hip, which of the following leg morphologies would favor a sprinter? A. massive thighs and slimmer lower legs B. massive lower legs and slimmer thighs C. leg morphology does not matter D. need more information

A

The statement "a rotating body will maintain a state of constant angular motion unless acted on by an external torque" refers to which of the following? A. Newton's first law of inertia B. Newton's second law of acceleration C. Newton's third law of action/reaction D. none of the above

A

What are the appropriate units for angular momentum? A. kg•m2/s B. kg•m/s2 C. kg2•m/s D. kg•m2

A

When a discus thrower spins and then releases the discus, what direction will it travel? A. tangent to the circular path at release B. tangent to the circular path at beginning of spin C. will continue in circular path D. need more information

A

Which of the following accurately describes the radius of gyration of the forearm segment? A. It is greater with respect to the wrist than with respect to the elbow. B. It is greater with respect to the elbow than with respect to the wrist. C. It is equal with respect to the wrist and with respect to the elbow. D. need more information

A

Which of the following is/are most important factor(s) affecting the magnitude of centripetal force? A. tangential linear velocity B. radius of rotation C. mass D. all of the above are equally important

A

Why do sprint coaches stress "heel to buttocks" during sprinting? A. reduces moment of inertia of the leg with respect to the hip B. reduces moment of inertia of the lower leg with respect to the knee C. reduces moment of inertia of the foot with respect to the ankle D. there is no scientific basis for this coaching cue

A

Why is a bat easier to swing if you grip the barrel instead of the handle? A. k is reduced B. k is increased C. moment of inertia is increased D. easier to grip the barrel

A

10. Somersaulting occurs around which of the following axes of rotation? A. frontal B. sagittal C. longitudinal D. all of the above

A frontal

If a diver goes from a full layout position to a tuck position, what will happen to her angular velocity? A. increase B. decrease C. remain the same D. need more information

A increase

newtons first law (rotational bodies)

A rotating body will maintain a state of constant rotational motion unless acted on by an external torque.

explain how angular momentum can be transferred from one axis to another

An airborne performer's angular velocity vector does not necessarily occur in t he same direction as the angular momentum vector. It is possible for a body's somersaulting angular momentum and its twisting angular momentum to be altered in midair, though the vector sum of two (the total angular momentum) remains constant in magnitude and direction.

Centrifugal force is a misnomer. What is really happening when you feel a pull to the outside while rounding a curve? A. centripetal force B. inertia C. both A and B D. none of the above

B

Which of the following quantities increases as moment of inertia decreases during the airborne phase of a dive? A. angular momentum B. angular velocity C. both A and B D. neither A nor B

B

Why are golf club heads weighted? A. to increase the moment of inertia of the club with respect to the shoulder B. to increase the moment of inertia of the club head rotating around the shaft C. to decrease the moment of inertia of the club with respect to the shoulder D. to decrease the moment of inertia of the club head rotating around the shaft

B

3. In the absence of external torque, which of the following will increase when moment of inertia decreases? A. angular momentum B. angular velocity C. both A & B D. none of the above

B angular velocity

When knee flexion is increased, what happens to the moment of inertia of the leg about the hip? A. increased B. decrease C. remains the same D. need more information

B decreased

Torque is the angular analogue of what? A. momentum B. force C. mass D. impulse

B force

Where is radius of gyration located in relation to center of gravity (COG)? A. closer to the axis B. further from the axis C. same distance from the axis D. need more information

B further from the axis

How come gravity does not affect angular momentum? A. d⊥ = 0 B. T = 0 C. both A and B D. gravity does affect angular momentum

C

If a pendulum stops swinging, which of the following is/are true? A. angular velocity = 0 B. angular momentum = 0 C. both A and B D. none of the above

C

Rotating around which of the following principal axes of rotation has the least moment of inertia (anatomical position)? A. transverse (frontal) B. anteroposterior (sagittal) C. longitudinal D. need more information

C

When a cyclist rounds a curve, where does centripetal force act? A. on the cyclist's center of gravity B. on the cycle's center of gravity C. on the tires of the cycle D. on the ground

C

Which of Newton's laws (angular analogues) explains why a batter wears cleats? A. 1st law - moment of inertia B. 2nd law - angular acceleration C. 3rd law - reaction D. none of the above

C

Which of the following acts to produce a change in angular momentum? A. moment of inertia B. torque C. angular impulse D. none of the above

C

Which of the following are accurate units for centripetal force? A. kg•m2/s B. kg•deg2/s C. N D. N-kg•m

C

Which of the following are accurate units for moment of inertia? A. N•m B. N•m2 C. kg•m2 D. kg•m

C

Which of the following is true of a baserunner weighing 70 Newtons and a baserunner weighing 50 Newtons? A. the centripetal force exerted on the heavier baserunner will be greater B. the heavier baserunner will not be able to run as fast around the bases, due to a greater centripetal force C. if the baserunners run at the same velocity around the bases, the heavier baserunner will have to lean in more towards the pitcher's mound due to a greater centripetal force D. all of the above are true

C

If a diver goes from a full layout position to a tuck position, what will happen to his momentum? A. increase B. decrease C. remain the same D. need more information

C-same

How can a cyclist maintain balance when rounding a sharp curve? A. slow down B. lean to the inside of the curve C. lean to the outside of the curve D. both A and B E. none of the above will affect balance

D

What effect does "choking up" on a bat have? A. reduces moment of inertia B. increases angular velocity of swing C. reduces mass D. both A and B E. all of the above

D

Which of the following is known as "center-seeking" force? A. momentum B. acceleration C. centrifugal force D. centripetal force

D

Which of the following is referred to as the "quantity of angular motion" possessed by a body? A. angular displacement B. angular velocity C. angular acceleration D. angular momentum

D

Which of the following is/are accurate formula(s) for angular momentum? A. H = Iω B. H = mk2ω C. M = mv D. both A and B E. all of the above

D

Which of the following variables affects angular momentum? A. linear velocity B. angular acceleration C. both A and B D. neither A nor B

D

Why does a figure skater cross his arms tightly across the chest when performing a quadruple axel? A. to reduce moment of inertia B. to increase angular velocity C. to increase time in the air D. both A and B E. all of the above

D

Which of the following variables contribute to moment of inertia? A. F and d B. T and t C. M and v D. m and k

D m and k

angular velocity centripetal force equation

Fc= mrw2 m-mass r=radius of rotation w-omega/angular velocity

tangential linear velocity centripetal force equation

Fc= mv2/ r fc=force m=mass v-tangential linear velocity r=radius of rotation

newtowns third law

For every torque exerted by one body on another, there is an equal and opposite torque exerted by the second body on the first. When a baseball player forcefully swings a bat, rotating the mass of the upper body, a torque is created around the player's longitudinal axis. If the batter's feet are not firmly planted, the lower body tends to rotate around the longitudinal axis in the opposite direction. However, since the feet usually are planted, the torque generated by the upper body is translated to the ground, where the earth generates a torque of equal magnitude and opposite direction on the cleats of the batter's shoes.

centripetal force

Force directed toward the center of rotation for a body in rotational motion

angular momentum

H=I (omega) H=(m)(k^2)(omega) angular momentum=(moment of inertia)(angular velocity)

angular momentum equation

H=I (w) w=omega/angular velocity i=moment of inertia (m x k^2) H-momentum=movement

moment of inertia equation and what it means

I=m (r^2) I=m (k^2) I=moment of inertia (the resistance to change) m=mass r/k=radius of rotation/gyration

equation for the moment of inertia for a body (human body) in respect to an axis

I=mk^2 I=moment of inertia m=mass k=radius of gyration

equation for moment of inertia

I=mr^2 I-moment of inertia m-mass (kg) r-radius of rotation from distributon of mass (m)

which axis is it easier to initiate rotation on?

It is easier to initiate rotation about the longitudinal principal axis than about either the mediolateral/transverse/frontal or the anteroposterior principal axes, because total body Momentum of inertia with respect to the longitudinal axis is much smaller than the body moments of inertia with respect to the other two axes.

principal moment of inertia (axis examples)

Principal moment of inertia:total body moment of inertia relative to one of the principal axes: the mediolateral/transverse (or frontal), the antero-posterior (or sagittal), or the longitudinal (or vertical), each of which passes through the total-body CG

what is decided about momentum at take off?

The magnitude and direction of the angular momentum vector for an airborne performer are established at the instant of takeoff.

conservation of angular momentum

The total angular momentum of a given system remains constant in the absence of external torques.

in the sagittal and frontal plane motion where is the axis passing through

axis passing through center of proximal joint

because of smaller moments of inertia, smaller gymnasts are _______ at performing rotations

better smaller moment of inertia, smaller resistance

during conservation of momentum, what can someone do to spin faster

decrease the radius of rotation, thus decreasing the I in the equation

what factor most dramatically influences angular momentum and why?

distribution of mass with respect to AOR (k) smaller k, smaller moment of inertia, smaller momentum

smaller moments of inertia= ______ to spin because

easier figure skaters bringing their arms in decreases moment of inertia because the radius of rotation is smaller meaning the inertia is decreased meaning the resistance to movement is decreased

linear impulse equation

force x time

the human body rotates _____ around _____ principle axes

human body rotates free of support, around 1/3 principle axes only 1 axis at a time

moment of inertia definition (angular)

initial property for rotating bodies, representing resistance to angular acceleration-based on both mass and distance of mass distributed from the AOR resistnace to movement. more inertia=harder to move

as mass increases or velocity increases, what happens to angular momentum

it also increases

once an object is airborne, what is true about angular momentum

it is conserved once the object is airborne

look over. lab 8

k

units of moment of inertia

kgm^2 Units of moment of inertia consist of mass multiplied by units of length squared

radius of gyration is much longer during what type of movements in the arm

longer with flexion/extension movements compared to supination/pronation

lower inertia means it is _______ to initiate movement, higher inertia means it is _______ to initiate movement

lower=easier higher-harder

Moment of inertia is the angular analogue of what? A. moment of force B. moment of time C. mass D. surface area

mass

more inertia (I) means

more resistance, harder to move

newtons second law

nA net torque produces angular acceleration of a body that is directly proportional to the magnitude of the torque, in the same direction as the torque, and inversely proportional to the body's moment of inertia. T = Iα. or α = T / I

moment of inertia is the _________ of the _______ of each particle's ______ and the_______

nMoment of inertia is the sum of the products of each particle's mass and radius of rotation squared I = Sum of (mr^2)

if a body has no angular velocity, is there angular momentum? why?

no. becuase angular momentum (H) =inertia (angular velocity)

is the radius of gyration the same as the segmental cg? does its length change?

not the same as the segmental cg -much longer than radius of rotation (segmental cg) because it is based on r^2 =length changes as the axis of rotation changes

linear momentum

product of mass and velocity

what factors are included in moment of angular inertia?

resistance to angular acceleration (definition) -mass -distribution of mass with respect to the axis of rotation

moment of inertia (linear)

resistance to linear acceleration. measured in terms of mass

according to newtowns secon dlaw, the greater the momentum of inertia is with respect to the axis of rotation at the elbow, the _______ is the resulting angular acceleration

smaller

Moment of inertia can only be defined with respect to a _____ axis of rotation.

specific

a body's inertia is directly proportional to what? what law does this demonstrate?

the body's mass. increased mass, leads to increased resistance to linear/angular acceleration -this is according to newton's second law

which has a larger impact on the angular inertia=the radius of rotation, or the actual mass?

the radius of rotation because it is squared in the equation

How many principle axes are there for the human body? A. one B. two C. three D. four

three c

Because angular momentum remains constant, a compensatory increase in angular velocity must accompany the decease in moment of inertia. give an example

tigher a diver's tuck, greater the. angular velocity same with a gymnast. they are able to turn alot faster in the air if they decrease their k, or radius of rotation/moment of inertia

angular impulse equation

torque (time)

principal moment of inertia

total body moment of inertia relative to one of the axes

can angular momentum be transferred from one principal axis of rotation to another?

yes

if you jump straight up, what is the angular momentum?

zero

what is the most influential factor on the magnitude of centripetal force?

•As is evident from both equations, the speed of rotation is the most influential factor on the magnitude of centripetal force, because centripetal force is proportional to the square of velocity or angular velocity.

procedures for changing the total body axis of rotation

•Asymmetrical arm movements •Rotation of the hips (termed hula movement) These asymmetrical movements can be used to generate twist and to eliminate twist. the lab standing on the turn table moving our arms to get it to start moving

what does change in momentum depend on?

•Changes in angular momentum depend not only on the magnitude and direction of acting external torques but also on the length of the time interval over which each torque acts.

what factors impact angular momentum?

•Mass (m), distribution of mass with respect to the axis of rotation (k) , angular velocity of the body (omega)

impulse momentum relationships

•Tt = change in H •Tt = I (change in w) •Tt = (Iw)2- (Iw)1 w=omega