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Particle Kinematics Course overview: Dynamics = Kinematics + Kinetics
Kinematics: The
description
of motion (position, velocity,
acceleration, time) without regard to forces.
Exam 1: (Chapter 12) Particle Kinematics Exam 2: (Chapter 16) Rigid Body Kinematics
Kinetics: Determining the
forces
(based on F=ma)
associated with motion.
Exam 3: F=ma (Particles and Rigid Bodies) Exam 4: Integrated forms of F=ma
(Work-Energy, Impulse-Momentum)
Particle: A point. Insignificant dimensions. Rotation not defined. Rigid Body: Infinite number of points. A RB may rotate, with
angular
displacement, velocity and acceleration.
Kinematic Variables
Particle kinematics involves describing a particle’s position,velocity and acceleration versus time.
PositionVelocityAccelerationTime
Vector
Scalar
r v a t
s v a t
Kinematic Variables
Description
Various Simple Coordinate Systems
x
y
z
s
r
s = distance along a
defined path
= position vector in a
coord system
r
Arbitrary Path
v
s
Circular Path
v x + s + 0
r Straight Line Path
v
Particle Straight Line (Rectilinear) Motion
0
x, s, v, a
Typical Rectilinear Motion Coordinate System
4
8
12
**-
-**
16
Key feature of straight line motion: Acceleration is alwayscollinear with the velocity. Examples:
Speed increasing.Speed decreasing.
Rectilinear Motion:
Accel always collinear with v. v
a
v
a
Particle Straight Line Motion
a = constant
a = f(t)
Straight Line Motion Cases:
a = f(v)
a = f(s)
v = f(s)
...etc...
Today!
Next class.
Various combinationsof the basic kinematicvariables a, v, s, and t. They all can beexpressed as functionsof another variable.
Straight Line Motion: Accel = Constant Case^ The defining kinematic equations may be integrated for accel =constant to get the familiar equations shown below. Memorizethese! You will use them often. Use them ONLY for accel =constant. (Do not plug an accel function into these eqns.)
Integrated (a = const)
Defining Eqns
Accel = Constant Equations
1
a
dvdt
v
dsdt
2 3
a ds
v dv
v = v
s = s
at
0
2
0
1 2
v
= v
0
2
2
Memorize
these! Use only fora = const!
Look for this wording: “accelerates uniformly”“accelerates at 4 m/s
” 2
“constant acceleration ”
Straight Line Motion: Accel = Constant Case^ See the example problems with this lecture for an example (ortwo) of acceleration = constant problems. Straight Line Motion: a = f(t) Case^ See the example problems with this lecture for an example pluskey principles you need to know. Next Class: Additional accel = function cases….^ (3) a = f(s)^ (4) a = f(v)^ (5) v = f(s)^ …etc…
