Angular Kinematics (Lecture 6)

angular motion

• axis of rotation

• a fixed Iine about which a body rotates

axis of rotation

a fixed line about which a body rotates

name the two types of sign conventions

clockwise and counterclockwise

clockwise rotations are _____

negative

counterclockwise rotations are ________

positive

angular position (𝜃)

how far a body is rotated from its reference

• radians

• degrees

radius

distance from the center to the perimeter of the circle

arc length (s)

• length of a curve

• distance between the 2 points along a section of curve

radian

ratio between arc length (s) and the (radius)

radian equation

s/r

• s: arc length

• r: radius

1 radian is _______

a measure of the central angle whose arc length equals the radius of the circle (s=r)

1 radian = (what’s the equation)

180°/π = 57.3

how do you convert degrees to radians?

multiply the number of degrees by π/180

(ex. 60° x π/180)

how do you convert radians to degrees?

multiply the number of radians by 180/π

angular displacement

change in angular position between 2 time periods of interest

angular displacement equation

θf-θi

angular velocity (𝜔)

how fast a body is rotating in a particular direction

angular velocity formula

𝜔 = ∆angular position/∆time

ex. 100 miles/2 hours = 50

angular acceleration (𝜶)

• time rate of change in angular velocity

• how quickly the object is speeding up or slowing down its rotation in a particular direction

angular acceleration formula

𝜶 = ∆ angular velocity/∆time