2. Particle vs. Rigid-Body Mechanics
What is the difference between particle and rigid-body mechanics?
Rigid-body can be of any shape
Block
Disc/wheel
Bar/member
Etc.
Can determine motion of any single particle (pt) in body
particle
Rigid-body (continuum of particles)

3. Types of Rigid-Body Motion
Kinematically speaking…
Translation
Orientation of AB constant
Rotation
All particles rotate about fixed axis
General Plane Motion (both)
Combination of both types of motion B A B A B A B A

4. Kinematics of TranslationB A y
Kinematics
Position
Velocity
Acceleration
True for all points in R.B. (follows particle kinematics) rB rA x

5. Rotation about a Fixed Axis – Angular Motion
Point P travels in circular path (whether “disk” or not)
Angular motion
Angular position, θ
Angular displacement, dθ
Angular velocity
ω=dθ/dt
Angular Acceleration
α=dω/dt r
Axis of rotation  

6. Rotation about a Fixed Axis – Angular Motion
Point P travels in circular path (whether “disk” or not)
Angular motion
Angular position, θ
Angular displacement, dθ
Angular velocity
ω=dθ/dt
Angular Acceleration
α=dω/dt
Angular motion Equations r
Axis of rotation  
In solving problems, once know ω & α, we can get velocity and acceleration of any point on body!!! (next slide)
(Or can relate the two types of motion if ω & α unknown )

7. Rotation about a Fixed Axis – Motion of Point
Point P travels in circular path
Position of P
Defined by r
If body rotates some dθ, then displacement is ds = r dθ
Velocity (tangent to path)
Acceleration (2 components) r an ∆v v a ∆v  a an  at an v

8. Example Problem
When the gear rotates 20 revolutions, it achieves an angular velocity of ω = 30 rad/s, starting from rest. Determine its constant angular acceleration and the time required. (F16-1, 3.58 rad/s2, 8.38 s)

9. Example Problem
The gear A on the drive shaft of the outboard motor has a radius of rA = 0.5 in and the meshed pinion gear B on the propeller shaft has a radius rB = 1.2 in. Determine the angular velocity of the popular in t = 1.5 s, if the drive shaft rotates with an angular acceleration a = (400t3) rad/s2 , where t is in seconds. The propeller is originally at rest and the motor frame does not move.