Particle Kinematics

1
Particle Kinematics
Inertial frame non accelerating, non rotating
reference frame Particle point mass at some
position in space
Position Vector
Velocity Vector

• Direction of velocity vector is parallel to path
• Magnitude of velocity vector is distance
  traveled / time

Acceleration Vector
2
Particle Kinematics

• Straight line motion with constant acceleration

• Simple Harmonic Motion

• Circular Motion at const speed

3
Summary

• General circular motion
• Arbitrary path

4
Summary

• Polar Coords

5
Newtons laws

• For a particle
• For a rigid body in motion without rotation, or a
  particle on a massless frame

You MUST take moments about center of mass
6
Calculating forces required to cause prescribed
motion of a particle

• Idealize system
• Free body diagram
• Kinematics
• Fma for each particle.
• (for rigid bodies or frames
  only)
• Solve for unknown forces or accelerations

7
Deriving Equations of Motion for particles

• 1. Idealize system
• 2. Introduce variables to describe motion(often
  x,y coords, but we will see other examples)
• 3. Write down r, differentiate to get a
• 4. Draw FBD
• 5.
• 6. If necessary, eliminate reaction forces
• 7. Result will be differential equations for
  coords defined in (2), e.g.
• 8. Identify initial conditions, and solve ODE

8
Motion of a projectile
9
Work and Energy relations
Rate of work done by a force (power developed by
force)
Total work done by a force
Kinetic energy
Power-kinetic energy relation
Work-kinetic energy relation
10
Potential energy
Potential energy of aconservative force (pair)
11
Energy relations for conservative systems
subjected to external forces
Internal Forces (forces exerted by one part of
the system on another)
External Forces (any other forces)
System is conservative if all internal forces are
conservative forces (or constraint forces)
Energy relation for a conservative system
Kinetic and potential energy at time
Kinetic and potential energy at time
Work done by external forces
12
Impulse-momentum relations
Impulse-momentum for a single particle
Linear Impulse of a force
Linear momentum of a particle
Impulse-momentum relations
Impulse-momentum for a system of particles
Total external impulse
Total linear momentum
Conservation law
13
Collisions
14
Angular Impulse-Momentum Equations for a Particle
Angular Impulse
Angular Momentum
Impulse-Momentum relations
Useful for central force problems