(a) One blade of a pair of scissors rotates clockwise in the xy plane. What is the direction of for the blade?
into the xy plane
out of the xy plane
clockwise
counterclockwise
(b) What is the direction of if the magnitude of the angular velocity is increasing in time?
into the xy plane
out of the xy plane
clockwise
counterclockwise
a) Into the xy plane
b) out of the xy plane
(a) To determine the direction of angular velocity for a blade of a pair of scissors rotating clockwise in the xy plane, imagine looking down from above the scissors. The direction of angular velocity is perpendicular to the plane of rotation and follows the right-hand rule.
The right-hand rule states that if you point your thumb in the direction of rotation, your fingers curl in the direction of the angular velocity vector. In this case, as the blade rotates clockwise in the xy plane, the angular velocity vector will point out of the xy plane. Therefore, the direction of the angular velocity vector for the rotating blade is out of the xy plane.
(b) If the magnitude of the angular velocity is increasing in time, the direction of angular velocity will depend on the specific situation.
If the angular velocity vector is pointing into the xy plane but its magnitude is increasing, it means the object is experiencing counterclockwise acceleration and its rotation is speeding up.
If the angular velocity vector is pointing out of the xy plane but its magnitude is increasing, it means the object is experiencing clockwise acceleration and its rotation is also speeding up.
So, the direction of the angular velocity vector depends on whether the object is rotating in a clockwise or counterclockwise direction in the xy plane.
In summary, the direction of the angular velocity vector depends on the specific rotation and whether the magnitude of the angular velocity is increasing or decreasing.
A) K(hat)
B) -K(hat)
12
(a) clockwise
(b) counterclockwise