Biomechanics - Exam 2 - Angular Acceleration

force * perpendicular distance to line of action

Formula for torque?

moment arm

What's the simple definition of "perpendicular distance to line of action"

the tendency (or effectiveness) of a force to cause rotation

What's the definition for torque (not formula)

torque

the tendency (or effectiveness) of a force to cause rotation

defines what

an off center force

Torque results from ?

translational and rotational

The result of torque is what 2 types of movement

vector

Torque is a scalar or vector quantity

force couples

Forces with equal magnitudes acting in opposite directions defines what

forces of the same magnitude acting in opposite directions

Define a force couple

pure rotation w/o tralnation

Force couples cause pure ________ with _____

mass and acceleration

Body weight is a product of ____ and ____ (due to gravity)

COM

What is this defining:

The point about which the sum of the external torques acting on the system equals zero

inertia

For safe measure, what is this defining

A bodies tendency to resist acceleration

T

The resistance to linear acceleration depends on an object's total mass

T or F

The distribution of mass has no impact on the resistance to linear acceleration

an objects resistance to resist angular acceleration

If inertia is defined as an objects tendency to resist acceleration, what is the definition of moment of inertia

an objects tendency to resist angular acceleration

Define moment of inertia

moment of inertia

Which depends on the distribution of mass, inertia or moment of inertia?

B

because the mass distribution is closer to the axis of rotation

Which is easier to swing, A or B? Why?

object with most at the beginning

Which object is easier to rotate, something with the most of its mass at the end of the object or something with most of its mass at the beginning of the object?

large moment of inertia = hard to rotate

If something has a large moment of inertia, is this easier to rotate or hard?

It brings the axis of rotation (your hands) closer to the distribution of mass, making this easier to swing

What does "choking up" on a baseball bat do?

each mass multiplied by the square of its distance from the axis, for everything in the object

this is the particle mass method

What is the formula for moment of inertia (mass particle method)

mass distribution around an axis

Radius of gyration denotes what

around an axis

Raidus of gyration denotes mass distribution ____ __ ___

radius of gyration

The distance from the axis of rotation where you could concentrate all the mass and still have the same moment of inertia.

This is a definition for what

I=mk^2

What is the formula for moment of inertia (not the particle mass method one) when expressed using the radius of gyration?

moment of inertia

Reducing the radius of gyration therefore reduces the ?

this decreases the radius of gyration and therefore decreases the moment of inertia

(this all makes it easier to swing the leg)

(this is why a straight leg feels heavy to swing, while a bent leg feels light)

Why does a sprinter flex their knee so much when running?

by moving the heavier components of the device near the proximal end, rather than having them at the distal end

With regard to prosthetics, how can you reduce the radius of gyration?

H is angular momentum

I is moment of inertia

w is angular velocity

this is the formula for angular momentum

H=Iw

What is this the formula for (what is H)

What is I and what is w

H=mk²w

What is the formula for angular momentum expressed in terms of radius of gyration?

external

angular

constant

When gravity is the only _____ force, then _____ momentum remains ____ during the flight (airborne activities)

does not change

During the flight phase in an airborne activity, does angular momentum change or not?

angular velocity

Manipulating moment of inertia results in changes in _____ ____

moment of inertia

Altering what results in changes in angular velocity

1. a rotating body will maintain a state of angular motion unless acted on by an external torque

2. torque=moment of inertia * angular acceleration (T=I*a)

3. for every torque, there is an equal and opposite torque

What are the angular analogs of the 3 laws of motion?

angular acceleration will go down

since T=I*a, rearranged this becomes a=T/I, so a is inversely related to i

In the angular analog of the 2nd law of motion, (torque = moment of inertia * angular acceleration), what happens to angular acceleration if the moment of inertia goes up?

angular acceleration will go up

since T=I*a, rearranged this becomes a=T/I, so a is proportionally related to T

In the angular analog of the 2nd law of motion, (torque = moment of inertia * angular acceleration), what happens to angular acceleration if the torque goes up?

linear: W=F*distance

W=F*d

angular: W=torque*angular displacement

W=T*𝚫θ

What is the formula for LINEAR work? Angular work?

RKE=1/2𝐼w²

If KE is 1/2mv², what is the formula for rotational kinetic energy?

1. translational kinetic energy

2. potential energy

3. rotational kinetic energy

4. strain energy

What are the 4 components of total energy?

TKE has a bigger magnitude than RKE

During running, a single segment can undergo large angular velocities. Is there more RKE or TKE associated with these segments?

P=torque * angular velocity

P=τ*ω

What is the formula for angular power?

linear: P=F*v

angular: P=τ*ω

Formula for linear power? Angular power?

torque τ

For the equations for angular motion, force (which is used with linear motion) is replaced with

linear momentum: when there is no net external force

angular momentum: when there is no net external torque

Under what conditions is a body's momentum constant? Angular momentum?

torque

Force is to linear as _____ is to angular