400882 Introduction to Biomechanics - Angular Kinetics

Define Moment of Inertia; provide its symbol/s and unit of measurement.

I = m x r²(Moment of inertia = mass x radius²)

Which has greater effect on the moment of inertia of a body: The total mass or where the mass is distributed relative to the axis of rotation?

The distribution relative to the axis of rotation has a greater effect than the total mass

The more closely mass is distributed to the axis of rotation, the easier it is to initiate or stop angular motion.

Why is it difficult to determine the moment of inertia for the body?

Because the body's moment of inertia is not fixed and changes. We don't know the distribution of fat/muscle within the segments

What is the radius of gyration?

Represents an objects mass distribution with respect to a given axis of rotation (it is not the same as the segmental COG)

Is the radius of gyration the same point as the COG for that segment?

No

Explain, with respect to moment of inertia, how and why children's sporting equipment varies from that of adults.

Because they have less mass making it lighter to pick up and also the mass distribution is closer to the axis of rotation compared to an adult version, reducing moment of inertia and making it easier for the child to swing

Explain which somatotypes (body shape and size) are suited to sports like gymnastics and diving.

...

Define Angular Momentum; provide its symbol/s and unit of measurement.

• Quantity of angular motion possessed in an object

• H = Iω → Angular momentum (H) = moment of inertia (I) x angular velocity (ω)

• Units kg.m²/s

• Vector determined by right hand rule

Can an object have angular momentum without any angular velocity?

No

What is meant by the principle of 'Conservation of Momentum'?

In the absence of external torques the total angular momentum of a system remains constant i.e. when gravity is the only external force

• As in projectile motion - angular momentum at take-off remains constant for duration of flight

Conservation of angular motion: an object will continue spinning with constant angular momentum unless acted on by an external torque

Explain how an athlete can transfer angular momentum from one axis of rotation to another.

Asymmetrical arm movements can tilt the axis of rotation out of its original position. E.g. diver changing from rotation in a somersault about the transverse axis into a twist around longitudinal axis

If angular momentum cannot be gained or lost once a body is rotating in the air, how then does a diver increase their rate of somersaulting during a dive?

By tucking tighter (closer to the transvers axis)

Define Angular Impulse.

• When a net torque acts: angular momentum of the system changes predictably

Depends on magnitude and direction of external torques and length of time.

• Angular impulse = Tt (torque x time) = change in angular momentum ΔH

• When angular impulse acts there is a change in the total angular momentum of the system

• Tt = ΔH

• Tt = (Iω)f - (Iω)i

T = torque

t = time

H = angular momentum

I = moment of inertia

ω = angular velocity

Explain the link between angular impulse and angular momentum.

You get angular momentum because of an angular impulse on take off

Define Angular Work, and provide its unit of measurement.

• Is defined as magnitude of torque against an object and the angular distance the object rotates in direction of applied torque

(remember: mechanical work = F x d)

• Angular work = T Δ θ

T = torque & Δ θ = change in angular distance

• Units (same as linear) = Nm or J

The angular work done by a muscle is either positive or negative. Differentiate between the two and indicate the muscle contraction types associated with each.

• +ve work is when torque due to muscle (e.g. biceps) is greater than torque due to load (e.g. dumbbell)

Concentric muscle action - shortening during work

• -ve work is when torque due to muscle is less than torque due to load

Eccentric muscle action

Note: We don't have a clear understanding of physiological cost related to mechanical work

Define Angular Power, and provide its unit of measurement.

• Angular power is defined as the product of torque and angular velocity

• Angular power = Tω (T = torque applied in Nm; ω = ang vel in rad/s) (linear Power = W/t)

• Units = Nm/s or watts

The Analogue of Newton's 1st Law of Motion states that ......

A rotating body will remain in a state of constant angular motion unless acted on by a net external torque

Give an example of the analogue of Newton's 1st law of motion.

Divers and gymnasts enabled to achieve aerial maneuvers by manipulation of I and angular velocity due to a constant angular momentum

The Analogue of Newton's 2nd Law of Motion states that ......

• A net torque produces angular acceleration in direct proportion to the magnitude of the torque and in the same direction as the torque, and angular acceleration is inversely proportional to the body's moment of inertia

• T = Iα(T = external torque; a = angular acceleration of object)

Give an example of the analogue of Newton's 2nd law of motion.

If person abducts arm from body in horizontal position

→ Torque at shoulder results in angular acceleration of arm

→ Greater I of arm about axis through shoulder and less angular acceleration of segment

The Analogue of Newton's 3rd Law of Motion states that ......

For every torque exerted by one body on another there is an equal and opposite torque exerted by the 2nd body on the first (torque produced by one body part to rotate that part results in counter torque by another body part)

Give an example of the analogue of Newton's 3rd law of motion.

Long jump

→ Swing legs forward and upward in prep for landing

→ To counteract lower body torque, the rest of the body has to move forward and downward

→ Produces torque equal and opposite to lower body

→ Angular velocity of 2 body sections are different because I is different