Chapter 9. Angular Motion in a Plane. ANGULAR DISPLACEMENT. Angular displacement ( q ) is usually expressed in radians, in degrees, or in revolutions. 6 segments gets to here. One radian is the angle subtended at the center of a circle by an arc equal in length to the radius of the circle.
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Angular Motion in a Plane
One radian is the angle subtended at the center of a circle by an arc equal in length to the radius of the circle.
2p segments gets completely around.
1 rev = 3600 = 2p radians (rad)
The radian measure of an angle is a dimensionless number.
The angular speed (w ) of an object whose axis of rotation is fixed is the rate at which its angular coordinate, the angular displacement q, changes with time. If q changes from qi to qf in a time t, then the average angular speed is
w = 2p f.
It is possible to associate a direction with w, and therefore with a, thereby specifying the angular acceleration vector a, but we will have no need to do so here.
aT is in the same direction of v.
If w gets smaller then v gets smaller.
aT is in the opposite direction of v.
Remember this slide
What is happening to the velocity of this point?
An object rotating about an axis tends to remain rotating at the same rate about the same axis unless interfered with by some external influence.
The sluggishness of an object to changes in its state of rotational motion
where w must be in rad/s.
The centripetal force (Fc) is the force that must act on a mass m moving in a circular path of radius r to give it the centripetal acceleration v2/r. From F = ma, we have
Where FC is directed toward the center of the circular path.