Can someone please provide me with some insight on this question?

A pair of scissors is being used to cut a string. Does each blade of the scissors have the same angular velocity (both magnitude and direction) at a given instant?
yes
no
Give your reasoning.

The answer is no. If both blades' magnitude and direction were the same, the blades would not close and the scissors would not cut. They would rotate tgether.

To understand why the answer is no, we need to consider the mechanics of scissors. Scissors consist of two blades connected at a pivot point. When we use scissors to cut a string, each blade moves in a circular motion around the pivot point.

At any given instant, the blades of the scissors do not have the same magnitude and direction of angular velocity. This is because the blades have different roles in the cutting process. One blade acts as the stationary arm, while the other blade is the moving arm that applies the cutting force.

As the stationary blade remains relatively fixed, the moving blade rotates around the pivot point to cut the string. The magnitude of the angular velocity of the moving blade is larger than that of the stationary blade because it covers a larger distance in a given time period.

Furthermore, the direction of the angular velocity is also different for each blade. The stationary blade's angular velocity is always zero since it doesn't rotate. However, the moving blade's angular velocity changes as it rotates around the pivot point.

Therefore, due to these differences in magnitude and direction, each blade of the scissors does not have the same angular velocity at a given instant.