Linear Impulse-Momentum Principle

 

Rigid bodies

 

Take a pencil and place it on a flat surface. Apply a force to the pencil that will make it roll straight. Then, apply a force to the pencil that will make it roll as well as rotate. What was the difference?

 

 

 

 

Principle of linear impulse and momentum: The impulse of the resultant force acting on a rigid body is equal to the change in the body's linear momentum. Note that the reference point is the body’s mass center.

 

∫∑F dt = mv_G,2 - ∑mv_G,1

 

Systems of rigid bodies

 

The total linear momentum of a system of rigid bodies is equal to the sum of the momenta of the individual bodies.

 

∫∑F dt = ∑m_iv_Gi,2 - ∑m_iv_Gi,1

 

Conservation of linear momentum

 

If the external forces acting on a rigid body sum to zero over a period of time, then the linear momentum of the body is constant.

 

∑m_iv_Gi,2 = ∑m_iv_Gi,1