Circular/Rotational Kinematics

Radian

Unit of measure for angles where one radian is defined as the angle where the arc length is equal to the radius

Angular position

Location of an object in an angular frame of reference, vector quantity

Angular position si unit of measure

radians (rad)

Angular displacement

an objects change in angular position, vector quantity 

angular displacement si unit of measure

radians (rad)

angular positionn symbol

θ with vector symbol

angular displacement symbol

Δ θ with vector symbol

how to write exact value

leave in terms of pi

arc length

distance along the circular path that an object travels during circular motion, scalar quantity

arc length symbol

s

arc length si unit of measure

meters

angular speed/velocity

rate that angular position changes with respect to time

angular speed symbol

ω

angular speed/velocity si units of measure

radians per second (rad/s)

tangential speed/velocity

the translational speed/velocity for an object at a point in time as the object travels along its circular path

Why do you not focus on average tangential speed/velocity

direction of tangential speed/velocity continuously changes

angular acceleration

rate that angular velocity changes with respect to time

angular acceleration symbol

α with vector symbol

tengential acceleration

the rate that tangential speed changes with respect to time, vector quantity

Why is tengential acceleration at a single point of time

direction continually changes

Tengtial acceleration symbol

aT

When velocity and acceleration have same direction

Speed increases

When velocity and acceleration have different directions

Speed decreases

Centripetal acceleration

acceleration responsible for changing the direction of vT

Centripetal acceleration symbol

ac

Where is centripetal acceleration direction towards

Towards the center of the circular path, perpendicular towards aT and ac

acceleration

2D vector, aT+ac

Angular/circular kinematic equations

Describes/models an objects circular/angular motion

angular acceleration si units of measure

rad/s²

tengential acceleratoin si unit of measure

m/s²

centripetal acceleration si unit of measure

m/s²