Angular Motion

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In subjects like Physics just as there are many formulas to calculate displacement and linear velocity and to calculate angular momentum  there are also equivalent formulas. This is great because we have an angular counterpart for many of the motions which are linear motion equations. In this article we will be discussing the relationship of angular motion with linear motion.

The angular motion which is simplest is one in which the body moves along a curved path at a constant angular velocity as for example when a runner travels along a path which is circular path or an automobile which rounds a curve. The very common problem here is to calculate the centrifugal forces and determine their effect on the object's motion.

A problem which is understood as very common while solving in many basic Physics texts books or texts which require determination of the maximum speed at which an automobile can round a curve and that too without skidding. We will solve this problem as it leads naturally to an analysis of running. Consider a weighted car of weight W which is moving on a curved level road that has a radius of curvature R.


Angular Velocity

There are two types of angular velocity one is whose orbital angular velocity and other spin angular velocity. Spin angular velocity refers to how fast a rigid object or body rotates with respect to its centre of rotation. Spin velocity of an angular object is said to be independent of the choice of its origin, in contrast to the above mentioned orbital angular velocity which readily depends on the origin choice.

In angular velocities which are said to be three dimensions the velocity is a pseudovector and with its magnitude also which is measuring the rate at which an object revolves or rotates its own direction which is already by this time pointing perpendicular to the instantaneous mentioned plane of angular displacement or rotation. The angular velocity orientation is conventionally specified by the rule of right-hand.

In the field of Kinematics we have studied motion along a straight line and introduced such concepts as the concept of displacement or velocity and acceleration. In the Two-Dimensional Kinematics it dealt with motion in two dimensions. Projectile motion is a very special case of two-dimensional kinematics in which the object is projected into the air while being the subject to the gravitational force and it lands a distance away. In this chapter we consider situations where the object does not land instead moves in a curved path. 


Rotational Angles 

If we see that when an object is rotating about its own axis at that time  some other  axis—for example when we take the example of  a CD that is a compact disc mentioned in  below rotates about its center—then each point in the object starts to follow a path which has a circular arc. Consider a line from the center of the CD to the edge of the cd. Each pit that plays a role in sound tracking is used to record sound along this line which moves through the same angle in the same amount of time. The angle of rotation is the amount of rotation and is analogous to linear distance as well. We hereby define the angle of rotation as Δθ which is said to be the ratio of the arc length to the radius of curvature that is: 

Δθ=Δvr

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Angular Velocity

Have we ever wondered that How fast an object is rotating? We define angular velocity as ω -as the rate of change of the angle. In symbols, this is written as: 

ω=Δθ/Δt

ω=Δθ/Δt

Here an angular rotation that is  Δθ takes place in a time Δt. The greater the rotation angles  in a given amount of time the greater the angular velocity is there. The units which are for angular velocity are radians per second  that is rad/s.

Angular velocity denoted as ω is analogous to linear velocity that is v. To get a very precise relationship between the linear velocity and the angular velocity, we shall again consider a pit on the rotating CD. This pit moves as an arc length that is Δs in a time that is  Δt, and so it has a linear velocity  which is written as:

v=Δs/Δt

 

Particles Which are Three Dimension 

In the space of three-dimensional particles we again have the position vector that is r of a moving particle. Here if we notice  as there are two directions which are perpendicular in nature to any plane which is an additional condition is necessary to uniquely specify the direction of the angular velocity which is conventionally the rule of right-hand used.

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Angular Velocity Vector for Rigid Body 

Given a rotating frame of three unit vector coordinates all the three must have the same angular speed at each point. In these frames each vector can be considered as a moving particle with constant scalar radius.

The rotating frame always appears in the context of rigid bodies, and special tools have been developed for the same purpose, the spin angular velocity may be described as an equivalent or vector as a tensor.

FAQ (Frequently Asked Questions)

Q1. Define Angular Motion?

Ans: Angular motion can be defined as, The motion of a body which is about a fixed point or axis. It is said to be equal to the angle which is passed over at the axis or point by a line drawn to the body.

Q2. State the Formula for Angular Velocity?

Ans: In uniform circular motion the angular velocity formula can be defined as angular velocity that is w is a vector quantity and is equal to the angular displacement that is Δθ, a vector quantity and divided by the change in time that is Δt. Speed is defined equal to the arc length traveled denoted by S which is divided by the change in time Δt which is also equal to |w|R.

Q3. In Circular Motion is the Angular Velocity Constant?

Ans:  While the object moves in a circle motion and at a speed which is constant speed, it undergoes linear constant acceleration so that it keeps moving in a circle. It's angular velocity is said to be constant since it continually sweeps out a constant arc length per time. Constant angular velocity in a circle is defined as the uniform circular motion.

Q4. What is Earth Angular Velocity?

Ans: If we look at it on the basis of the sidereal day the Earth's true angular velocity that is  ω Earth is said to be equal to 15.04108⁰/mean solar hour that is 360⁰/23 hours 56 minutes 4 seconds. ωEarth can also be expressed in radians/second form that is rad/s by using the relationship of ωEarth = 2*π /T where T is defined as the Earth's sidereal period that is 23 hours 56 minutes 4 seconds.