KIN 3514 - angular kinematics

what is angular motion?

refers to motion around an axis of rotation; ex: spins, swings, twists, or rotates around an axis of rotation; All parts of the body move in a circle, through the same angle around a single axis of rotation, but do not undergo the same linear displacement

what does 1 radian equal in degrees?

57.3 degrees

what is the circumference of a circle in radians?

2pi rad

how do you find theta in radians?

theta in radians = arc length/radius = s/r

what are absolute angles (segment angles)

The angle between a segment and the right horizontal of the distal end

what are relative angles (joint angles)?

The angle between the longitudinal axis of two adjacent segments; Straight fully extended position is generally defined as 0 degrees  (or can be 180)

what is needed for the relative angle of the hip joint?

positive angle for flexion & negative angle for extension

what is needed for the relative angle of the knee joint?

positive for flexion & negative for extension

what is needed for the relative angle of the ankle joint?

positive for dorsiflexion & negative for plantar flexion

what do you use to calculate absolute angles?

arctangent (inverse tangent) function

what do you do when the absolute angle relative to the right horizontal is in quadrant 1?

keep the angle the same (degree is already positive)

what do you do when the absolute angle relative to the right horizontal is in quadrant 2?

add 180 (degree is already negative)

what do you do when the absolute angle relative to the right horizontal is in quadrant 3?

add 180 (degree is already positive)

what do you do when the absolute angle relative to the right horizontal is in quadrant 4?

add 360 (degree is already negative)

what are the ways for calculate relative angles?

1) Law of Cosine (useful if you have the segment lengths, or points for 3 joints)

2) Two absolute angles to find relative angles (useful if you have two absolute angles)

relative angles can be determined from _______

absolute angles

what is used to show the direction of angular motion?

right-hand thumb rule

the right-hand rule is when the ______

curled fingers of the right-hand point in the direction of the rotation, direction of the extended thumb point to the direction of the vector

what rotation indicate positive angles in angular motion?

counter-clockwise rotation

what rotation indicate negative angles in angular motion?

clockwise rotation

what is the formula for angular displacement?

∆𝜃 = 𝜃_𝑓  −  𝜃_𝑖

what is angular displacement?

defines the change in angular position; the difference between the initial and final angular positions of the rotating object; (Can be measured in degrees (°) or radians (rad)

what indicates negative angles in angular displacement?

clockwise rotation

what indicates positive angles in angular displacement?

counter-clockwise rotation

true or false: If the object travels 1 or more full rotations, those rotations must be included in the displacement

true

when is this formula (theta = s/r) valid?

when expressed in radians

what is angular distance?

Sum of the magnitude of all angular changes undergone by a rotating body (Scalar); degrees(°)orradians(rad)

what is angular velocity?

How fast the angle is changing; The vector rate of change of angular displacement; ex: a bike tire, a record player, a power drill, a ceiling fan, etc

what are the units for angular velocity (𝜔)?

deg/s or rad/s

true or false: The greater the rotation angle in a given amount of time, the greater the angular velocity

true

what is tangential velocity?

the instantaneous linear velocity of an object in rotational motion; 𝑣_𝑡

when is the formula (𝑣_𝑡  = 𝑟𝜔) for tangential velocity valid?

only valid if w is expressed in rad/sec

what is Angular Acceleration (α)?

how quickly angular velocity is increasing or decreasing; 𝛼 is the rate of change of angular velocity 𝜔

what is the formula for Angular Acceleration (α)?

𝛼 =∆ω/∆𝑡

what are the units for angular acceleration?

rad/s² & deg/s²

what is Tangential Acceleration (a_𝒕)?

the linear acceleration resulting from angular acceleration

when is the formula (a_𝑡 = 𝑟α) for Tangential Acceleration (a_𝒕) valid?

only valid if α is expressed in rad/sec²

what does the object need to move in a curve path?

inward acceleration toward the center of the   curve. Without this, it will result in a straight-line motion

what needs to occur in centripetal (radial) acceleration?

Rotation requires acceleration of the object to change the direction of linear velocity

what is Centripetal (Radial) Acceleration (𝒂_c or 𝒂_r)?

towards the center of rotation & perpendicular to the circular motion; ensures that the object keeps moving in a curved trajectory, constantly changing its direction to stay on the path; does not change the speed (magnitude of velocity) of the object. If an object is   moving at a constant speed along a circular path, centripetal acceleration does not make it go faster or   slower. It merely maintains the object's circular motion

what is the relationship between these formulas: a_c = 𝑣²/r & a_c=ω²r

If 𝑣 is kept constant, 𝑎_c is inversely proportional to r

a_c is proportional to v² and w²

If ω is kept constant, a_c is proportional to r