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I am assuming that an angular velocity vector only has two direction: positive for counterclockwise and negative for clockwise.

Just to make sure that I have the right interpretation.

Newton's 1st law states:

An object remains in a state of uniform rotational motion unless acted upon by a net torque. ("In a straight line" is taken out)

This means that the speed of the angular velocity vector is constant. However, even without an net torque, the direction will change. how?

Edit. I just googled Newton's 1st Law. It only says uniform motion in a straight line. Does it mean the object can travel back and forth along the line?

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    $\begingroup$ Understand the vector of angular momentum better, here: physics.stackexchange.com/q/219890 . Newton's 1st applies to pure rotation as it does to pure translation. $\endgroup$
    – Gert
    Nov 22, 2015 at 16:14
  • $\begingroup$ @Gert, how to we measure the angle between the force and position vectors? Sin270 will be -1. $\endgroup$ Nov 22, 2015 at 17:41
  • $\begingroup$ I'm not sure what you mean. So $\sin 270^\circ=-1$, so what? $\endgroup$
    – Gert
    Nov 22, 2015 at 17:52
  • $\begingroup$ @Gert, my book did not limit the range of theta to [0, 180]. (Formula: t=rFsintheta) $\endgroup$ Nov 22, 2015 at 17:53
  • $\begingroup$ It doesn't have to: an angle is an angle is an angle, period. $\endgroup$
    – Gert
    Nov 22, 2015 at 18:02

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By uniform motion in a straight line, the law refers to both its magnitude and direction. You can't go back and forth without a force.

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