Term
| Angular interpretation of Newtons Second Law |
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Definition
For rigid Bodies: If a net external torque is exerted on an object, the object will accelerate angularly in the direction of the net external torque, and its angular accelleration will be directly proportional to the net external torque and is ineversely proportional to its moment of inertia
For Linear Motion
–If a net external force is exerted on an object, the object will accelerate in the direction of the net external force, and its acceleration will be proportional to the net external force and inversely proportional to its mass
For Angular Motion
–The change in angular momentum of an object is proportional to the net external torque exerted on it, and this change is in the direction of the net external torque
For Non-Rigid Bodies
–Variable moment of inertia
–A net external torque acting will cause a change in angular momentum
–The change in angular momentum may be
seen as
(1) a speeding up or slowing down of the object's angular velocity,
(2) a change in the direction of the axis of rotation, or
(3) a change in the moment of inertia.
The angular acceleration of the object or a change in its moment of inertia does not necessarily indicate the presence of a net external torque, The total angular momentum of a non-rigid object may remain constant even if it angularly accelerates or if its moment of inertia changes. |
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Term
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Definition
What is work?
It is the means by which energy is transferred from one object or system to another
The unit of measurement is the Joule, J |
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Term
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Definition
What is Energy?
In mechanics, energy is defined as the
ability to do work
Energy comes in many forms:
heat
light
sound
chemical
mechanical |
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Term
| Forms of Mechanical Energy |
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Definition
Kinetic Energy
Energy due to motion
A moving object has the ability to do work because of its motion
The unit of measurement is the Joule, J
Potential Energy
Energy due to position
Two Types
Gravitational Potential Energy & Strain Energy
Gravitational Potential Energy (GPE)
Potential energy due to an object’s position relative to the earth
Gravitational potential energy of an object is related to its mass(m)
mass(m)and the height of the object (h)
The unit of measurement is the Joule, J
Strain Potential Energy
Potential energy due to the deformation of an object
Strain potential energy of an object is related to its material properties (k) and the amount of deformation (x)
The unit of measurement is the Joule, J |
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Term
| Work--Energy Relationship |
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Definition
The unit of measure for work and
energy is Joules
Work is the means by which energy
is transferred from one object to
another object |
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Term
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Definition
The work done by external forces
(other than weight) acting on an object causes a change in energy of the object |
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Term
| Conservation of Mechanical Energy |
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Definition
When is Mechanical Energy Conserved?
When no external forces, other than
weight, act on the body
If there are no external forces, other than weight, acting on the body, NO WORK is done
If no work is done, the total mechanical
energy of the object is conserved (i.e., it cannot be changed; it remains constant)
Thus, it can be used to analyze
situations in which no work is done
For instance, in the pole vault, the
vaulter does no work during the vault
itself (i.e., once he or she leaves the
ground) |
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Term
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Definition
The rate of doing work or how much work is done in a specific amount of time
It can also be thought of as how quickly or slowly work is done
The unit of measurement is the Watt, W
average force times average velocity (Fv) along the line of action of that force |
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Term
| Kinetic energy (equation) |
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Definition
| ke = 1/2mv2 = 1/2 mass (m) * velocity squared (v2) |
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Term
| Angular Velocity (equation) |
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Definition
| w =^0/t = Of - Oi/t = angualr displacment / time |
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Term
| Strain potential energy (equation) |
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Definition
| SPE = 1/2kx2 = 1/2 material property (k) * deformation (x)2 |
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Term
| Angular Impulse (momemtum) (equation) |
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Definition
| Tt = Hf - Hi = Torque*time (F*Dperp) Angular momementum final (IfWf) - Angular Momemtum Initial (IiWi) |
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Term
| Angular Acceleration (equation) |
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Definition
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Term
| Tangential acceleration (equation) |
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Definition
| at = ar = tangential acceleration (at) = instant angular acceleration * radius of rotation |
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Term
| Gravitational potential energy (equation) |
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Definition
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Term
| Angular Momemtum (equation) |
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Definition
| H = IW = Angular (H) = Inertia (I) * angular velocity (w) |
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Term
| Moment of inertia (equation) |
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Definition
| I = {miri2 = moment of inertia (I) sum of: mass intial (mi)* radius initial squared (ri2) |
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Term
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Definition
| T = F(dperp) = torque (T) = Force (F) * perpendicular distance or moment arm (dperp) |
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Term
| Centripital Acceleration (equation) |
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Definition
| ar = v2T/r or w2r = centripital force (ar) instant angular velocity squared (v2t) / radius or angular velocity squared (w2) * radius (r) |
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Term
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Definition
| U = F(d) = work (U) = Force (F) * Distance (d) |
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Term
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Definition
| P = U/^t = F(^d)/^t = F (^d/^t) = Fv; power (p) = work (u)/ change in time (^t) = Force (F) * Change in Distance (^d)/ change in time (^t) = Force (f) * distance (d) / time (t) |
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Term
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Definition
An imaginary point which represents the
axis of rotation of the body unless
the body is constrained to rotate about an externally defined axis of rotation |
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Term
| Center of gravity of the human body |
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Definition
When the body is in anatomical reference position
Changing the center of gravity by
changing the orientation of body
segments |
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Term
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Definition
“The turning effect produced by a force
is called a torque.” |
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Term
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Definition
An external force directed through the
center of gravity of an object
The effect of a centric force is to cause a change in the linear motion of the object |
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Term
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Definition
An external force not directed through the center of gravity of an object
The effect of an eccentric force is to cause a change in the linear and angular motions of an object |
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Term
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Definition
A pair forces equal in size but opposite in direction and noncolinear
The effect of a force couple is to cause a change only in the angular motion of an object
The resultant of the two forces in a force couple is a force of zero |
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Term
Mathematical Definition of Torque
What influences the magnitude of a
torque and how is torque quantified? |
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Definition
Torque is directly related to the size of
the force that creates it
Torque is also influenced by; the position and orientation of the line of
action of the force and the axis of rotation |
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Term
Mathematical Definition of Torque
Expanded Definition of Torque |
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Definition
| A torque is the turning effect produced by a force and is equal to the product of the magnitude of the force and the moment arm |
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Term
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Definition
The distance between the line of action of the force and a line perpendicular to it that passes through the axis of rotation
The unit of measurement is a meter (m)
Also known as the perpendicular distance |
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Term
| Conditions of Static Equilibrium |
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Definition
Net force equals zero
Net torque equals zero |
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Term
| Factors affecting stability |
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Definition
Height of c.g.
Base of support
Weight of object |
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Term
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Definition
An angle is formed by the intersection of two lines, two planes, or a line and plane
Angular Units of Measure Radians (rad) |
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Term
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Definition
| The orientation of a line with respect to another line or to a plane |
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Term
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Definition
Angular displacement is the change in absolute angular position experienced by a rotating line It is the angle formed between the finalangular position and the initial angular position of a rotating line
It is a vector
Counter-clockwise rotation = positive direction
Clockwise rotation = negative direction |
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Term
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Definition
The curvilinear distance (l)traveled by a point on a rotating object is
directly proportional to; the angular displacement of the object
and the radius (r), the distance that
point is from the axis of rotation of
the object.
If the angular displacement is measured
in radians, the curvilinear distance
traveled is equal to the product
of the angular displacement and the
radius.
The unit of measurement is a meter |
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Term
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Definition
Average angular velocity is the rate of change of angular displacement
Unit of Measurement radians per second (rad/s)
vector
Instantaneous Angular Velocity (w) |
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Term
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Definition
Averageangular acceleration is the rate of change of angular velocity
Angular acceleration occurs when
something spins faster and faster or
slower and slower, or when the spinning
object's axis of spin changes direction
radians per second squared (rad/s2)
A vector
InstantaneousAngular Acceleration (a) |
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Term
| Tangential Acceleration (aT) |
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Definition
The component of linear acceleration
tangent to the circular path of a point on a rotating object
This is a type of linear acceleration
The unit of measurement is a meter per second squared (m/s2) |
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Term
Centripetal Acceleration (or radial acceleration) |
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Definition
a point on a rotating object experience linear acceleration even if the object spins in place The unit of measurement is a meter per second squared (m/s2) linear acceleration occurs if something speeds up, slows down, or changes direction This linear acceleration is directed toward the axis of rotation |
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Term
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Definition
The property of an object to resist
changes in its angular motion is
angular inertia
Factors Affecting Angular Inertia
–Mass
–Distribution of Mass Relative to the Axis of Rotation |
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Term
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Definition
The amount of inertia of an object
The effects of mass and the distribution of mass are not equal
The unit of measurement is a kilogram meter squared (kg-m2) |
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Term
Moments of Inertia about Different
Axes |
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Definition
An object may have more than one
moment of inertia, because an object
may rotate about more than one axis of
rotation. |
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Term
| Manipulating the Moments of Inertia of the Human Body |
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Definition
–Body movements may change the
distribution of mass about an axis of
rotation, thus changing the moment of
inertia about that axis
––A human's moment of inertia about any
axis is variable |
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Term
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Definition
For rigid objects, changes in angular momentum depend on changes in only one variable
-angular velocity
For linked-rigid bodies, however, changes in angular momentum may result from changes in angular velocity or changes in moment of inertia, or both
A vector
-The direction of angular momentum is the same as the direction of the angular velocity that defines it
Unit of Measurement kilogram meter squared per second (kg-m2/s) |
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Term
Angular Interpretation of
Newton’s First Law |
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Definition
For linear motion,
–Every body continues in its state of rest, or of uniform motion in a straight line, unless it is
compelled to change that state by forces impressed upon it
The angular equivalent of Newton's first law may be stated as follows:
–The angular momentum of an object remains constant unless a net external torque is exerted on it.
For a rigid object
–Moments of inertia are constant
–This law implies that the angular
velocity remains constant
For a system of linked rigid bodies
–the body's moment of inertia is variable
–can be changed by altering limb
positions
–the body's angular velocity also changes
Newton's first law does not require
that the angular velocity be constant
But rather that angular momentum
be constant if no external torques act |
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Term
| Angular Impulse and Angular Momentum |
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Definition
angular impulse = change in angular
momentum
The unit of measurement for angular
impulse is a Newton meter second (Nm-s)
The unit of measurement for angular
momentum is a kilogram meter squared
per second (kg--m2/s) |
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Term
| Angular Interpretation of Newton’s Third Law |
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Definition
For Linear Motion
–For every force exerted by one body on another, the other body exerts an equal force back on the first body but in the opposite direction
For Angular Motion
–For every torque exerted by one object on another, the other object exerts an equal torque back on the first object but in the opposite direction
–The torques acting on the two objects have the same axis of rotation |
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