Angular Impulse-Momentum Principle

 

Explain what happens when your take you finger and spin a fan blade.

 

 

The impulse of the resultant moment (applied by your finger) acting on a body is equal to the change in the body's angular momentum (spinning of the blades).

 

Pure translation

 

Translation with respect to a fixed-point O.

 

∫∑M_O dt = r_G/O,2 x mv₂ - r_G/O,1 x mv₁

 

Pure rotation

 

Rotation about fixed-axis through point O.

 

∫∑M_O = I_O,2ω₂ - I_O,1ω₁

 

General planar motion

 

General planar motion with respect to the body's mass center.

 

∫∑M_G = I_G,2ω₂ - I_G,1ω₁

 

General planar motion with respect to a fixed-axis through point O.

 

∫∑M_O = r_G/O,2 x mv_G,2 + I_G,2ω₂ - r_G/O,1 x mv_G,1 + I_G,1ω₁