angular kinematics

What is angular motion?

Rotation of a body/segment about an axis; points trace circular arcs around that axis.

How are linear and angular motion related?

Points on a rotating body have linear motion tied to its angular motion.

What is motion capture?

Technologies that record positions/angles over time

Examples of motion capture

Multi camera optical systems, high speed video

Relative angles

Measure the angle between two connected body segments or parts

relative angle example

angle between your thigh and lower leg at the knee

absolute angles

measure the angle of a single body segment of reference line against a fixed external reference

absolute angles examples

the angle of the thigh segment relative to a horizontal line

Where both relative and absolute angles would be needed 

Vertical jump or sprint start: absolute trunk/pelvis orientation + relative hip/knee/ankle angles to interpret technique, performance, and loading.

Angle/position

θ (rad or °)

Displacement

Δθ (rad or °)

Velocity

ω=Δd/Δt (rad x s^−1, ° x s^−1)

Acceleration

α=Δω/Δt (rad x s^-2, °x s^−2)

Time

t (s)

Three units for angular motion

Radians, degrees, revolutions (1 rev = 360° = 2π rad)

Angular distance

a scalar quantity that represents the total angle or total path covered during rotation

Angular displacement

a vector quantity that measures the change in angular position from an initial to final point , including both magnitude and direction

Angular velocity

a vector quantity with both magnitude and direction (axis of rotation)

Angular speed

a scalar quantity representing only the magnitude (how fast the object is rotation)

Right-hand rule (RHR)

Curl right-hand fingers in rotation direction; thumb points along positive axis.

Prerequisites of RHR

defined coordinate axes and which rotation sense is positive.

Is clockwise positive or negative?

negative

Is counterclockwise positive or nagative?

Positive

When is angular acceleration positive?

when the rotation is speeding up counter-clockwise or slowing down clockwise

When is angular acceleration negative?

when the rotation is speeding up clockwise or slowing down counter-clockwise

When is angular acceleration zero?

When the object is rotating at a constant angular velocity

What is the relationship between angular and linear velocity?

linear velocity equals radius x angular velocity

What step must be completed prior to calculating the relationship between linear and angular velocity?

Specify the exact point of interest and its radius rr from the rotation axis, and convert ω (angular velocity) to rad/s with consistent units.

How does changing the radius affect linear velocity of an object after release when angular velocity is held constant?

increasing radius increases the velocity

Is take-off linear velocity of the ball, the same as the linear velocity of the bat at the contact point? Why?

No, the ball's velocity will be the result of a collision between the incoming ball and the moving bat, and the ball's final velocity depends on the relative velocities and masses of the two objects

Gravity

9.8m/s²