Why angular velocity is vector

Rotating wheel: Consider a bicycle wheel with handles attached to it, as in. Suppose the person holding the wheel tries to rotate it as in the figure. Her natural expectation is that the wheel will rotate in the direction she pushes it, however, what happens is quite different. The forces exerted create a torque that is horizontal toward the person, and this torque creates a change in angular momentum L in the same direction, perpendicular to the original angular momentum L, thus changing the direction of L but not the magnitude of L.

The axis of the wheel has thus moved perpendicular to the forces exerted on it, instead of in the expected direction. Gyroscopic Effect : In figure a , a person holding the spinning bike wheel lifts it with her right hand and pushes down with her left hand in an attempt to rotate the wheel.

This action creates a torque directly toward her. The wheel moves toward the person, perpendicular to the forces she exerts on it. Gyroscope: This same logic explains the behavior of gyroscopes see. There are two forces acting on a spinning gyroscope. The torque produced is perpendicular to the angular momentum, thus the direction of the angular momentum is changed, but not its magnitude. The gyroscope precesses around a vertical axis, since the torque is always horizontal and perpendicular to L.

Gyroscopes : As seen in figure a , the forces on a spinning gyroscope are its weight and the supporting force from the stand. Gyroscopes serve as rotational sensors. For this reason, applications of gyroscopes include inertial navigation systems where magnetic compasses would not work as in the Hubble telescope or would not be precise enough as in ICBMs.

Another application is the stabilization of flying vehicles, such as radio-controlled helicopters or unmanned aerial vehicles.

Privacy Policy. The direction of the angular acceleration is co-linear with the axis of rotation and the right-hand rule gives the rotational direction of the angular acceleration. Which statement is correct regarding an ant on a disk that is rotating slower and slower as illustrated? Section A1.

In this case, the direction of rotation is counter clockwise when looking at the page the direction that the fingers curl , so the rotation vector points out of the page the direction of the thumb. This is really just a consequence of the fact that 3 components in 3D is a coincidence. There are two axis where velocity and acceleration travel in a theta pulls a particle to the center of the curve just like the normal acceleration in a car pull you into the curve.

Ar in the picture really changes the direction. The angular velocity should be on the axis of rotation because the axis are all arbitrary and you can make them where it is easiest to solve. You can derive the angular rotation vector from trigonometry if you trying to track the changes of a vector that rides on a rotating body. It is a vector because it conveys magnitude and direction for the rotation. Tt also obeys the regular rules of vector algebra.

It can be multiplied with a scalar and it can added to other rotations vectors. Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. Why is angular velocity a vector quantity?

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