KINE 3050: Angular Kinematics

angular motion

*Body parts DON'T move in the same directions/distances

*Move around a fixed axis

joints

Where do body limbs exhibit angular motion?

*Around our ___

angles

Measures of the orientation of 2 lines or planes that intersect

relative angle

included angle between two segments

*Between 2 body segments

absolute angle

angular orientation of a body segment with respect to a fixed line of reference

radian

What is the SI unit for angular displacement?

radian, angle, length, radius

____: the size of the ___ that is EQUAL in ___ to the ___ of the circle

2pi, full

What is the radius of a circle circumference

*___ rotation

57.3 degrees

How many degrees are in each radian?

*___ degrees = 1 radian

center of rotation

the point about which a figure is rotated

fulcrum

What is the center of rotation of a LEVER?

instantaneous center of rotation

the center of rotation at a specific instant in time during movement

position, displacement, velocity, acceleration, angular

What are the ANGULAR kinematic variables?

*Just in the ___ version

acceleration

What causes the change in angular velocity?

velocity

What causes the change in angular displacement?

angular displacement

Change in angular position

vector

Is angular displacement a vector or a scalar?

clockwise & counterclockwise, no

What 2 directions could be used for angular displacement?

*Is this ideal for human movement?

direction, person, viewer

Angular displacement ____ depends on the position of the ___ being viewed and the position of the ___

right-hand rule

What should you use to find the direction of angular movements?

upward, right, front, positive

In right-hand rule, your THUMB should always point ___, to the __ or in __ of the body

*Always in the POSITIVE direction

rotation, same, fingers, positive

If the movement ___ is in the ___ direction that the ___ are curling, then the movement is ___

*Right-hand rule

opposite, fingers, negative

Rotation that is ___ the direction that the ___ are curling is considered ____

angular velocity

rate of angular displacement

*Angular displacement/time

average angular velocity

Represents the ENTIRE movement within a time period

instantaneous angular velocity

Represents 2 TIME POINTS that can be infinitesimally close or further apart

*Rate of rotation at an INSTANT in time

angular acceleration

Rate of change of angular velocity

deg/s or rad/s

What is the SI unit for angular velocity?

360 degrees

How many degrees are in a revolution?

up, transverse

Which way to you point your thumb when dealing with a movement using the LONGITUDINAL axis?

*What plane will movements be in/what plane is the axis PERPENDICULAR to?

right, sagittal

Which way to you point your thumb when dealing with a movement using the MEDIAL-LATERAL axis?

*What plane will movements be in/what plane is the axis PERPENDICULAR to?

forward, frontal

Which way to you point your thumb when dealing with a movement using the ANTERIOPOSTERIOR axis?

*What plane will movements be in/what plane is the axis PERPENDICULAR to?

angular, angle/axis

In ___ motion, all parts of a body move through the SAME __/___

revolution, 360

When you do one ___ (turn or twist), you complete ___ degrees rotation

one radian

One arc length equals __ ___

2pi radians

One radius equals ___ ___

radian, instantaneous, radius, angle

____ is the ___ POSITION of the object executing a circular orbit of ___ is most conveniently specified in terms of ___ (theta)

theta = s/r

Ratio between arc length & the radius

arc length, radius, radian

___ ___ = ___ when theta = 1 ____

pi/180 x degrees

Conversion for radians

180/pi x radians

Conversion for degrees

absolute, external, reference, anti-clockwise, right horizontal

___ angle:

*Measured from ___ frame of ___

*Most usual convention is the measure the ANGLE _____ from the __ ___

absolute, position, fixed, immovable, horizontal, vertical

___ angular ____:

*One line or plane is ___ & ___ relative to earth

*Orientation of a body part to the ___ or ___

relative, position, lines, planes, moving

___ angular ___

*Both ___ or ___ are capable of ___

joint angle

Angle between 2 body segments

viewing position

What must you specify when finding the DIRECTION of angular displacement?

delta theta = final position - initial position

Angular displacement equation

*Described by theta

direction of rotation

For the right-hand rule, the FINGERS represent what?

axis of rotation, positive

For the right-hand rule, the THUMB represents the __ __ __ in a ___ direction

axis of rotation, greater

A point FARTHER from the ___ __ __ travels a ___ LINEAR distance than a point CLOSER to it

angular position

Defines an object's position relative to a defined spatial reference system

arc length = angular displacement(radius)

Relationship between linear & angular displacement EQUATION

*Meters

*Radians

*Meters

w = theta/t

Angular velocity equation:

*rad/s

*Angular displacement

*Time

revolution

Particle travels ALL the way around the circle

2pi, 360

What is the ANGLE of a full circle in RADIANS?

*Equals ___ degrees

linear, larger, greater

For ___ motion, a particle with ___ velocity undergoes a ___ displacement

direct, uniform circular

What is the relationship between angular velocity & angular displacement?

*Happens in __ __ motion

displacement, second

Angular velocity is the angular ___ through which the particle moves each ___

farther, linear speed, instantaneous linear velocity, closer

Points ___ from an axis of rotation travel at a GREATER __ __ & GREATER __ ___ __ than points ___ to an axis of rotation

tangential linear velocity

linear velocity of a point on a rotating segment

direction, tangent, circular, rotating

The ___ for tangential linear velocity is ___ to the ___ path of the __ point

wr

What is the magnitude for tangential linear velocity

*Angular velocity

*Rotation

rad/s^2 or deg/s^2

What is the SI unit for angular acceleration?

axis of rotation, positive, positive

Right-hand rule:

*Align thumb w/ __ __ __ in ___ direction

*Fingers of right hand curl in the ___ direction of rotation

speeding up or starting

What (2) scenarios occur when angular acceleration is in the DIRECTION of angular motion?

slowing down or stopping

What (2) scenarios occur when angular acceleration is in the DIRECTION OPPOSITE of angular motion?

faster

When sign of velocity & sign of acceleration are the SAME, body is rotating ___

slower

When sign of velocity & sign of acceleration are the OPPOSITE, body is rotating ___

direct

What is the relationship between angular velocity & tangential linear velocity

tangential acceleration

Component of linear acceleration TANGENTIAL to circular path

centripetal/radial acceleration

Component of linear acceleration to the CENTER(radius) of a circular path

aT = rα

tangential acceleration equation

w^2r or vT^2/r

Centripetal acceleration equations

direction, tangential

Centripetal acceleration focuses on the change in ___ of ___ velocity

magnitude, tangential

Tangential acceleration focuses on the change in ___ of ___ velocity

points, linearly, directions

If released at different __ on the path, object will travel __ in different ___

tangential velocity, circular, constant, direction

The __ __ of an object moving on a ___ path at a ___ angular velocity changes ___ from point to point

linear acceleration

Occurs when object slows down, speeds up or changes directions

centripetal, axis of rotation, center

___ acceleration:

*Acceleration directed toward the ___ or __ of circular path

centripetal force, center, path

Centripetal acceleration caused by the ___ ___ towards the ___ of the __

direct

What is the relationship between centripetal/radial acceleration & radius when ANGULAR VELOCITY is constant?

inverse

What is the relationship between centripetal/radial acceleration & radius when TANGENITAL VELOCITY is constant?

centripetal/radial, inside, outside

The ___/___ acceleration is GREATER running on __ line compared to ___ lane

force, centripetal force

What causes the change in linear velocity?

What changes angular velocity?

angular displacement, angular velocity, angular acceleration

What are the concepts of rotational kinematics?

vertex, intersection

A point where two or more straight lines meet.

*Also called ___

2 lines/planes & vertex/intersection

What are the 2 components of an ANGLE?

180 degrees

How many degrees are in pi radians?

arc length

the distance between the endpoints along an arc measured in linear units

2pi radians, 360 degrees

What is the answer if the ARC LENGTH is thefull revolution of a circle in RADIANS?

*What about in degrees?

theta 1

What is the absolute angle in Quadrant 1?

-theta 1

What is the absolute angle in Quadrant 2?

*Considered theta 2

theta 3 + 180

What is the absolute angle in Quadrant 3?

-(theta 4 + 360)

What is the absolute angle in Quadrant 4?

Nascar, less, work, tires

In what sport is it good to be closer to the axis of rotation?

*Has ___ angular displacement

*Produces less ___ on the ___

quadrants

What should you add to your angular displacement diagram to make it easier to determine the angle?

*Need end & start lines

tangential, perpendicular, centripetal acceleration

___ velocity is always ___ to the ___ of the circular path

centripetal, center, radius

___ force goes to the ___ of a circle

*Similar to ___

1/360

What does a degree represent in circumference?

l = theta*r

Equation for linear distance

*Angular displacement

*Radius