Lecture 4 - Angular Kinematics 1

Draw equivalent position-time, velocity-time, and acceleration-time graphs

Or inverse

Velocity is equal to the slope of the….

position-time curve

Acceleration is equal to the slope of the…

velocity-time curve

Position is equal to the area of the…

velocity-time curve

Velocity is equal to the area of the…

acceleration-time curve

Angular Kinematics

Study of angular/circular motion, describes the motion; measuring movement along a circular path about a line or fixed axis; body travels through same angle, in same direction, in same period of time.

• Quantities similar to linear kinematics, but unit of measurement changes (radians and degrees)

• Angular displacement, velocity, and acceleration

Angular Displacement (θ)

The angle through which a body has rotate about an axis

• Size of a circle can change, angle will not

• θ = s/r [radians]

When r = arc length (s), θ = …

1 radian

If s < r →

θ < 1 radian

If s > r →

θ > 1 radian

Circle Circumference =

2πr = 360°

1 rad =

180/π = 57.3°

Final angular position must…

reflect number of rotations that occured

Every revolution =

360° or 2π radians

Angular Velocity

The rate of change of angular displacement

• ω = (Δθ)/(Δt) = (θ_f - θ_i)/(Δt) [rad/s or °/s]

• Direction determined by right hand rule

Right Hand Rule

Used to determine direction of motion for angular quantities

• Curl right hand about the rotating axis, ringers pointing in the direction of rotation; extending thumb points in the direction of the angular velocity

Angular Acceleration

The rate of change of angular velocity over time

• 𝛼_avg = (Δω)/(Δt) = (ω_f - ω_i)/(Δt) [rad/s² or °/s²]

• Direction determined by right hand rule