L13 Flashcards
Angular motion occurrs when:
All parts of a body move through the same angle but do not undergo the same linear displacement
Angular kinematic describes
Angular motion without regard to the causes of the motion
Most human motion is a result of
Angular motion of the limbs that occur around joints
Degree: one circle/ one complete rotation
360 degrees
Revolution/ Number of rotations per one circle
One revelution
Radian: one circle= 2 pi radians
1 rad= 57.3 degrees
How to convert degrees to radians: ex 50 degrees
50 degrees/ x = 360 degrees/ 2 pi rad
-divide the degrees by x, equal it to 360 divided by 2 pir, then cross multiply to get 2pirad x 50 =360(x), solve for x by dividing 50 x 2pi radians by 360
How to convert radians to revolutions: ex 10 radians
10 rad/ x = 2 pi radians/ 1
-cross multiply to get 2 pi rad x (x) =1 (10 rad), so divide 1 (10rad) by 2 pi radians
How to convert revolutions to degrees: ex 3.3 revolutions
3.3rev/ x = 1rev/ 360 degrees
-cross multiply to get (3.3)(360) = 1(x), then divide by 1 to isolate x
Angular position
Orientation of a line with another line or plane
Absolute angular position (angle)
Angle of a single body segment with respect to a known vertical or horizontal
Ex) angle of the trunk is calculated with respect to the vertical plane
Relative Angular Position (angle)
-angle of one refment relative to another
-angle between longitudinal axes of 2 segments
Ex) angle of the trunk is calculated with respect to the knee, hip, and torso
Absolute segment angles
Calculated using tan
Tan: the ratio of the side opposite the angle and the size adjacent to the angle
TOA
Absolute Segment values calculated using
Tan= TOA
(Yproximal- Ydistal) / (Xproximal- X distal)
Relative angles use:
Law of Cosine
-relationship between the side of a triangle that doesn’t contain a right angle
CAH
-adjacent/ hypotenuse
Relative angles: law of Cosines uses:
Pythagoreans theorem
A= square root of (Xprox- X dist) squared + (Yprox- Ydist) squared
-need to use for all 3 side lengths of a triangle
Then: find cos for angle of triangle
Axis of rotation
-fixed line about which a rigid body rotates
-always perpendicular to its plane
Axis of Rotation
-direction of a rotation of angular motion referred to as the polarity of the vector
Right Hand Rule
-fingers curl the same direction as the rotation of the limb trying to determine the rotation of
-if thumb is pointing right or up, it is positive
-if thumb is left or down, it is negative
Angular distance is
The sumn of all angular changes (scalar)
Angular Displacement is:
The difference between the final and initial positions (vector)
Angular Displacement calculated by:
Change in angle= angle final- angle initial
Ex) 170 degrees- 5 degrees
Final change in angle= 165 degrees
Linear displacement of a point on a rotating object or rigid body is directly proportional to
The distance that point is from the axis of rotation
-the greater the radius, the greater the linear displacement
Linear Displacement
L= change in angle x radius
L= length of arc
Change in angle= angle measured in radians
R= radius
The larger the radius of rotation (r),
The greater the linear distance travelled by a point of a rotating object or rigid body
Angular speed
The angular distance travelled per unit of time as a scalar quantity
Angular velocity
Omega (w)
-vector quantity that describes the time rate of change of angular position (in rad/s or degrees/ s)
W= change in angle/ change in time
(Final angle- initial angle)/ change in time
Average Angular Velocity
Calculated anglular velocity for the object or rigid body through a certain angular displacement
Instantaneous Angular Velocity
Calculated angular velocity at a specific instant when an object or rigid body is rotating
Angular Acceleration
Alpha (weird a)
-rate of change in angular velocity measured inn radians per second squared or in degrees per second squared
Alpha= change in angular velocity/ change in time
(Final angular velocity- initial angular velocity) / change in time
