Pure Translation

 

Translation of a rigid body

 

 

Referring to the above figure, why can the ball be modeled as a particle? Why does the car need to be modeled as a rigid body?

 

 

 

 

What would happen if N_front went away?

 

 

 

 

Newton's second law for a rigid body

 

If a rigid body is rotating, different locations on a rigid body may have different accelerations. This is why the acceleration in Newton's second law is the acceleration of the body's center of mass. However, when a body is only translating, the acceleration of every point on the body will be the same.

 

∑F = ma_G

 

Moment equation for a rigid body

 

The sum of the moments acting on a rigid body undergoing pure translation is non-zero unless the reference point is the center of mass (G). If the moments are summed about an arbitrary point P, the resultant moment will equal the "moment" that the effective force (ma) creates about P (see figure). Note that this is not a real moment, but it is a convenient way to think about it.

 

 

∑M_P = r_G/P x ma     or     ∑M_G = 0