Question

1. We have previously established that Newton's Laws are only valid in inertial references frames. How can we modify Newton's Laws (particularly the 2nd law) to make them work in noninertial reference frames?

2. What is an angular velocity vector? Calculate the magnitude and direction of the Earth's angular velocity vector.

Answer 1

1] A non-inertial reference frame is one which is accelerating with respect to an inertial frame. Newton's laws are only valid in inertial reference frames and so to describe the motion of objects in a non-inertial reference frame, an additional force, which is a pseudo-force, must be added to account for the observed motion of the object from the inertial frame. Eg: Centrifugal force or Coriolis force.  

This extra force is absorbed in the net force F_net so that the equation F_net = ma still retains the same form.

2]

Angular velocity is the rate of change of angular displacement with time. The angular velocity vector in a way specifies the direction of rotation of the body. It is determined using the right-hand rule. If the body is rotating counter-clockwise, then the angular velocity vector will be directed outwards perpendicular to the plane of rotation.

its magnitude is related to the time period as:

for Earth's rotation about its own axis, the time period for 1 rotation is:

T = 60 x 60 x 24 = 86400 s

therefore, .