can anyone explian angular displacement?

Question

is it the very very small distance/displacement of a particle in rotational motion or can it be of any distance in the path of the body cause if it is then we cannot compare it with linear motion since neither is the velocity nor the displacement constant during the motion please help im really confused here

my question is how can θ be vector quantity since it does not travel in a particular direction secondly v from which omega is derived is only when a body has one direction but here the particle rotates

is wat willismg trying to say is (s*r)=theta where both s and r are vectors is infact (s.r)? if that is true then how come to get omega we call it a vector?

Answer 1

[Additional Details]
It seems your question has three parts:
i) "why are θ,omega,alpha vector quantities, and what is the meaning of them having a direction?"
ii) "with particular reference to (uniform) circular motion"
iii) "ditto the meaning of s,v having a vector direction"

i) The answer is that their vector direction is the axis of rotation, which will be perpendicular to the plane of the rotation (for planar rotation anyway). Think of them as a scalar attached to a direction. It's a convention.

ii) [5 days ago: my question is how can θ be vector quantity since it does not travel in a particular direction secondly v from which omega is derived is only when a body has one direction but here the particle rotates]

When talking about (uniform) circular motion, |v|=omega²/r
At any instantaneous moment, linear velocity v is tangential to the circle.
Thus the only direction to which v is always tangent is n, the axis of rotation, which is perpendicular to the entire plane of rotation.

In this context it is most meaningful to talk of linear displacement s as a scalar, because if you do a vector integral
s = Integ dv/dt
along one full revolution you will get zero displacement (obviously), which is not what you want.
So think of it that the tangential direction of v is not very relevant.

[5 days ago: is wat willismg trying to say is (s*r)=theta where both s and r are vectors is infact (s.r)? if that is true then how come to get omega we call it a vector?]
Like I said consider it a scalar with a direction attached.

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I really don't see what the confusion is, the laws of linear and angular motion are just:

Linear displacement: s
Linear velocity: v=ds/dt
Linear acceleration: a=dv/dt = d²s/dt²


Angular displacement: θ (theta), or phi or whatever
Angular velocity: omega=dθ/dt
Angular acceleration: alpha=d(omega)/dt = d²θ/dt²

So if the quantities involved are all constants you get the familiar forms:
s = ut + ½at²
θ = omega*t + ½alpha*t²

> can it be of any distance in the path of the body
Yes. Displacement means distance from whatever reference point you chose. (Maybe your reference point is stationary or maybe it is also rotating at some angular velocity. You simply pick whatever frame of reference makes your life easiest. Both have their virtues. This arises in mechanics, electronic engineering etc.)

>cause if it is then we cannot compare it with linear motion since neither is the velocity nor the displacement constant during the motion

Why not, they're directly comparable!
Of course displacement isn't constant during the motion.
Velocity might or might not be constant, if it isn't then that's equivalent to saying there is angular (de/)acceleration.
This is totally analogous to the linear case.
(Maybe you're thinking of the simpler case of uniform linear motion?)

>please help im really confused here

Still don't see where there's anything to be confused about, unless you mean "what is angular acceleration?"
Maybe you can give a numerical example and explain what you find confusing?

Answer 2

In Rectilinear motion, there is Displacement, Velocity and Acceleration. The displacement is the disstance travelled during a certain time interval. measured in meters The Velocity is the rate at which this distance is covered, expressed in meters per second The Acceleration is the rate of change in the velocity (up or down ). If the velocity is not consstant but increasing of decreasing at some rate. this rate of increase or decrease in the velocity is called Acceleration , can be plus or minus and expressed in units of meters/ Sic^2 For angular motion,, the displacement is expressed in Radians.. A radiuan is the angle that has the length of the arc equal to the length of the radius or Radian = S/R where S is the length of the arc and Ris the length of the Radius of that arc. The radian is therefore dimensionless because it is meters/ meters, inches/ inches or feet/feet etx. If you take the circumference of a circle and roll it out in a straight line and measure how many segment of a lenth equal to the radius does it contain you will find it contains a little over 6 segmnts., or exactly 6,28 segments which is = 2pi Circumference = 2 pi R and Circumference/R = 2 pi So the number of Radians for a full circle or one complete revelution is 2 pi . One revolution is 360 degrees and that is equal to 2 pi Radians or 6/28 Radians which makes a radian 360.6.28 = 57.32 degrees. Circular motion is Rotation. The Velocity ( called Omega) is Displacement / Time or Rad/ sec Sometimes the Velocity is expressed in Revolution per minute called RPM and expressed as N The relation ship between Rev/min and Rad per sec is Omega (Rsf?sec) = 2pi N /60 where N is the RPM THE Linear Velocity of a point on the surface of the wheel that has angular motion is V= (Omega) R and is tangent to the circular path.and expressed in meters/ sec. Think of it as a particle of mud that flies away from the tires while iit is rotating. It flies off tangent to the tire at that point. The angular Acceleration has two components one is called Normal Acceleration and the other is called Tangential. The Normal Acceleration is always present if there iis circular motion even if the angular velocity is constant. It it a vector directed towards twhe center of rotation is expressed as An = (Omega)^2 R in units of meters/Sec^2 The Tangential Acceleration is only present if the angular velocity(Omega) is changing , The change in the angular Velocity with respect to time is called Angular acceleration (Alpha) = d(Omega)/dt and expressed in Rad/sec^2 The tangential acceleration of a point on the surface is At = R (alpha) and is expressed in m/s^2 and has a direction tangent to the path. If Omega is constant , this acceleration does not exiist.

Answer 3

As it turns out, there are two ways that something can "move". It can slide around from one place to another. And it can spin. It can also do both at the same time, and both have to be accounted for. Think of a record (or a CD, I guess, for most of you). Look at the label and pick out something on the label: some word or even better, some letter.

If you're trying to follow that letter around as the CD moves around, you have to keep track of both where the CD slides around to and how much it spins.

Angular displacement keeps track of how much it spins, and linear displacement keeps track of how much it slides. Both of these types of motion follow the same types of formulas for constant acceleration.

However, the way you get around the direction changing problem is to have a reference frame that moves and even accelerates. Such accelerated reference frames lead to things like the so-called centrifugal force, which isn't really a force at all, but merely our mind playing tricks on us when we're in an accelerating reference frame, like in a car going around a bend.

Linear displacement is a vector, but angular displacement is NOT a vector, technically speaking. For something to be a vector quantity, you must be able to do two changes in a row in either order and get the same result (vector addition is commutative). For instance, if you go one block west, then one block north, it gets you to the same place as if you go one block north first, then one block west.

For angular displacement (in more than one dimension), this does not happen. If you lay a book on the desk in front of you (like you were going to open it and read it) and spin it a quarter turn (90 degrees) clockwise on the desk, then flip it up towards you 90 degrees you see the spine of the book on the top and the cover towards you.

If you do these two spins the other way around, first flip it up towards you, then spin it clockwise, the spine is on the side away from you, and the cover is facing to your left.

I'm tired now, so I'll stop. If you are in a physics class, ask your teacher and maybe they can explain it better.

Answer 4

Angular displacement is measured in degrees, radians or revolutions. It can not be a distance!