Noninertial Mechanics

SI units & Physics constants

Noninertial mechanics investigates relative motion of objects inside noninertial reference frames

Here (all units see here):

x, y, z is noninertial reference frame with origin at point O

x', y', z' is inertial reference frame with origin at point O'

m is mass of object

 is position  vector of noninertial frame with respect to inertial frame

 is position vector of object with respect to noninertial frame

 is position vector of object with respect to inertial frame

 is relative velocity of noninertial frame with respect to inertial frame

 is relative velocity of object with respect to noninertial frame

 is relative linear acceleration of object with respect to noninertial frame

 is linear acceleration of noninertial frame

 is angular velocity of noninertial frame

 is angular acceleration of noninertial frame

General formulas

Noninertial reference frame is a frame of reference which is moving with acceleration

Absolute position vector of object is its position with respect to inertial frame given by vector sum

Velocity of noninertial frame

Relative velocity of object

Acceleration of noninertial frame

Relative acceleration of object

Absolute velocity and acceleration

Velocity of transportation motion is absolute velocity of the point where the object is at the given instant with respect to inertial frame

where  is vector product of vectors  and

Acceleration of transportation motion is absolute acceleration of the point where the object is at the given instant with respect to inertial frame

Coriolis acceleration

Absolute velocity of object with respect to inertial frame

Absolute acceleration of object with respect to inertial frame

Fictitious forces

Total fictious force acting on object in noninertial reference frame

Newton's Second Law for motion of object in noninertial reference frame

where  is resultant force of all real forces acting on the object from other bodies

Fictitious force in translating reference frame

 Where:

 m is mass of object

 is acceleration of the system

 is net external force applied from other bodies

 is fictitious force due to acceleration

 is relative acceleration of the object with respect to the system

The fictitious force acting on the object due to acceleration

Equation for motion of the object inside the system

Fictitious forces in rotating reference frame

Where:

 is angular velocity of the system

 is angular acceleration of the system

 is radius of rotation of the object

 is relative velocity of the object with respect to the system

The fictitious force acting on the object due to angular acceleration is given by vector product

The centrifugal force due to angular velocity

The Coriolis force due to Coriolis acceleration

Equation for motion of object inside the rotating system under the influence of fictious forces

where is real net external force applied from other bodies