Is angular dispacement a vector?

Question

If it is a vector give its direction.

Answer 1

yes it is a vector for anticlockwise rotation it is perpendicular upwards and for clockwise perpendicular inwards but always along the axis of rotation..but this can be applied only if anhular displacement is small...for large angular displacement it is scalar as angular displacement doesn't obey laws of vector addition if angle is large

Answer 2

A quantity is a vector if it is understood only when its direction is given.

But to know the direction of a quantity, there must be an initial direction with reference to which the direction of the quantity can be ascertained.

But always the initial direction is intuitively understood even though it is not specified.

Given a direction, to find another direction we must know the angle through which the direction has turned.

Thus from the initial direction and the angle through which the direction has changed we find the direction of the quantity.

When a point moves along a straight line, the linear displacement is the change in position between the initial and final positions; here even though the direction is not given it is understood that it is in a direction from the initial to final point along the straight line. The angle through which the direction has changed is zero.

Suppose in the above example if I say that the direction changes through an angle ‘A’, the angular ‘displacement’ is the angle A. Now the question is whether this angle is a vector?

The question which has gone astray is, “In which plane the angle has to be measured?” As usual , intuitively, we assume some plane and the concept of direction is lost.

Thus, if the plane in which the angle to be measured is not given, we cannot talk about the angle.

In order to specify a plane, a line (a direction) perpendicular to the plane is taken as reference. If in the plane an initial direction is rotated clockwise then the direction of plane is said to be toward us from the plane along the axis of rotation and if turned anticlockwise the direction is away from us along the axis of rotation.

If we curl the right hand fingers (except the thumb) in the direction of rotation of the initial direction then the thumb gives the direction.

A plane perpendicular to the thumb is identified.

Thus the angle of rotation has both magnitude and direction and direction is the direction of the plane of rotation. The direction of plane is found using the above rule. A plane has two directions.

The angular displacement is a vector.

Answer 3

Yes, but not for the reasons others have given.

It is a vector because it has direction and a magnitude. If it is a counterclockwise angular displacement, its direction is called positive. If clockwise, it is called negative. Its magnitude is the number of degrees (or radians) through which the vector to which it is applied rotates.

It can also be thought of as a vector operator. In the sense that translation corresponds to the 'addition' of a pair of vectors, rotation can also be thought of as 'multiplication' of a vector by a 'unit vector' located at the origin of the coordinate frame. That is, a vector of the form (a+jb) where a^2 + b^2 = 1 (in the 2 dimensional case. It extends very naturally to higher dimensions)

Note that this is only the 'normal' product, not the 'dot' (or 'inner') product nor the 'cross' (or 'outer') product. Those are quite different things.


Doug

Answer 4

I savour your question and learn from Calzrhe's answer. I positioned my answer in a different way. look while an gadgets is moving in a plane and that i ask you to uniquely detrmine that plane wherein it is moving by ability of a vector what's going to you go with. As Calzrhe says, a perpendicular course to the plane seems teh handy way, yet there are 2 perpendiculars, so we've convention to define ?Xr as v, the place ?, r and v are all vectors. Now coming on your 2d question specific there is a few thing, quite yet another stressful vector in that course referred to as angular momentum, Vector L defined as rXp, the place p is the linear momentum vector. by ability of determining like this we've have been given some form of analogous similarity between linear and angular action. in case you stretch the analogy too plenty then there are a number of stressful issues you will face. yet pl are not getting aggravated use it and attempt to appreciate teh annoyance. As Feynman says approximately QM take it with no attention that it particularly works please do not ask why because of fact no person knows it! Intricacies of physics start up precise in classical Physics it self. you say not something is occurring in perpendicular course. ok, take rotating wheel on an axle carry the axle on your 2 palms. Wheel is rotating not something is occurring alongside the axle. Now attempt rotate the axle and experience which you hit upon subject in balancing your self. So after all some thing is factor is there in perpendicular course and that someting additionally facilitates the wheel to rotate because it rotates.

Answer 5

yes (curl the fingers of your right hand along the direction of the rotational motion and the direction is defined to be given by your right thumb. if something moves by a multiple of 2 pi radians (including zero radians), then angular displacement is described by the zero vector whose direction is undefined.)

Answer 6

ang. displacement=angle turned/time is a vector and the change occurs in the direction of the angle.

Answer 7

Yes it is. Displacement is always vector!