Angular Kinematics Equations

Question 1

Angular Distance

Answer 1

• Scalar quantity
• Total angular change
• Units: deg, º, rad, rev
• φ = angular distance

Question 2

Angular Displacement

Answer 2

• Vector quantity
• Change in angular position.
• Formula: θ = angle2 - angle1

Question 3

Angular Speed

Answer 3

• σ (sigma)
• Scalar quantity.
• angular distance/change in time.
• σ = φ/t- φ = angular distance

Question 4

Angular Velocity

Answer 4

• Rate of change in angular position
• Change in angular position/change in time
• ω (omega)
• ω = θ/t
• ω = θ2 - θ1/t2 - t1

Question 5

Angular Acceleration

Answer 5

• Rate of change in angular velocity
• α (alpha)
• Change in angular velocity/change in time
• The angular acceleration may be positive, negative, or zero (deg/s², rad/s²).
• α = (ω2 - ω1) / (t2 - t1)
• α = Δω / Δt

Question 6

Angular and Linear Distance Conversion

Answer 6

• l = rφ
• l is linear distance
• r is radius of rotation
• φ (phi) is angular distance

Question 7

Angular and Linear Displacement Conversion

Answer 7

• d = rθ
• d is linear displacement
• r is radius of rotation
• θ is angular displacement

Question 8

Angular and Linear Speed Conversion

Answer 8

• s = rσ
• s is linear speed
• r is radius of rotation
• σ (sigma) is angular speed

Question 9

Angular and Linear Velocity Conversion

Answer 9

• v = rω
• v is linear velocity
• r is radius of rotation
• ω (omega) is angular velocity

Question 10

Angular and Linear Acceleration

Answer 10

Angular acceleration may be resolved into 2 perpendicular linear acceleration components:

• Tangential acceleration
• Radial acceleration

Question 11

Tangential Acceleration

Answer 11

• Component of acceleration of a body in angular motion directed along a tangent to the path of motion
• Represents change in linear speed
• at = rα

Question 12

Radial Acceleration

Answer 12

• Component of acceleration of a body in angular motion directed toward the center of curvature
• Represents change in direction
• ar = v^2/r