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Chapter 2 of 7

Dynamics of Particles and Rigid Bodies

Dynamics extends statics by considering bodies in motion and the forces that cause that motion. The foundation is built on Newton's three laws of motion. The first law states that a body remains at rest or in uniform motion unless acted upon by a net external force. The second law relates the net force to mass and acceleration through \(F = ma\). The third law asserts that for every action there is an equal and opposite reaction, \(F_{12} = -F_{21}\).

Two important theorems follow from Newton's laws. The work-energy theorem states that the net work done on a body equals its change in kinetic energy, \(W_{net} = \Delta KE = \tfrac{1}{2}mv_2^2 - \tfrac{1}{2}mv_1^2\). The impulse-momentum theorem states that the impulse (force multiplied by time) equals the change in momentum, \(F\Delta t = \Delta(mv)\), where linear momentum itself is defined as \(p = mv\). It is important to distinguish kinematics, which describes motion without regard to its causes, from kinetics, which relates forces to the resulting motion.

For rotational motion, angular velocity \(\omega = d\theta/dt\) is the rate of change of angular displacement, measured in rad/s. A body moving along a circular path experiences centripetal acceleration directed toward the center, given by \(a_c = v^2/r = \omega^2 r\). D'Alembert's principle provides a useful bridge between dynamics and statics: by introducing an inertial force equal to \(-ma\) into a dynamic system, the problem can be analyzed as if it were in static equilibrium.

All chapters
  1. 1Statics and Equilibrium
  2. 2Dynamics of Particles and Rigid Bodies
  3. 3Thermodynamics
  4. 4Fluid Mechanics
  5. 5Mechanics of Materials
  6. 6Heat Transfer
  7. 7Machine Design, Manufacturing, and Units

Drill it

Reading is not remembering. These come from the Mechanical Engineering Basics deck:

Q

What is the first condition of equilibrium in statics?

The sum of all forces acting on a body must equal zero: ΣF = 0.

Q

What is the second condition of equilibrium in statics?

The sum of all moments about any point must equal zero: ΣM = 0.

Q

What is a free body diagram (FBD)?

A sketch of a body isolated from its surroundings showing all external forces and moments acting on it.

Q

What is a statically determinate structure?

A structure where all unknown reactions can be found using the equations of equilibrium alone.