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
