Pure Rotation or Rotation about a Fixed Axis

 

 

Rotation about a fixed axis is also called pure rotation. This results in all points on the body moving in a circular paths around the central fixed axis. All points on the body, except the points along the fixed axis, may experience linear and angular acceleration.

 

 

 

Newton's second law for pure rotation

 

∑F = ma_G

 

Now that each point on the body may experience a different acceleration, unlike the case for pure translation, we must take care to use the acceleration of the body's mass center (G) in Newton's second law. We can use the following kinematic relationship to determine the acceleration of G.

 

a_G = α x r_G/O - ω²r_G/O

 

 

Moment equation for pure rotation

 

∑M_O = I_Oα

 

Note that the moments and mass moment of inertia are with respect to the fixed-axis through O.