Engr Help

Summary -Important Principles (Impulse and Momentum)

Integration of Euler’s Second law

Σ M_C = I^C_zz α

Euler’s Second Law

with respect to time yields the principle of angular impulse and momentum –

(Note rotational acceleration about z-axis.)

t₂

∫ Σ M_C k dt = I^C_zz ω₂ k - I^C_zz ω₁ k

t₁

Principle of Angular Impulse and Momentum

The angular impulse acting on a body equals its change in angular momentum during the time

of the angular impulse. Here

t₂

∫ Σ M_C k dt = the angular impulse acting on the body from t₁ to t₂

t₁

Σ M_C = sum of moments of all external forces about the center of mass and all

external couples

I^C_zz = mass moment of inertia of body about its mass center, C

ω₂ = angular speed at time t₂ , ω₁ = angular speed at time t₁

Next consider the case where integration of Euler’s Laws are with respect to displacement.

The result will yield the principle of work and energy namely the work done by all forces and moments, actually doing work, equals the change in kinetic energy of the system.

Click here to continue with Summary.

Return to Notes on Dynamics