[Physics Class Notes] on Angular Motion Pdf for Exam

In Physics, there are various formulas for calculating linear velocity, and displacement and for calculating the angular momentum you can find equivalent formulae. Here we will be discussing the relationship between angular motion and linear motion. The angular motion is the motion where the body moves along the curved path at a constant and consistent angular velocity. An example is when a runner travels along the circular path or the automobile that goes around the curve. One of the common issues here is calculating centrifugal forces and determining its impact on the motion of the object.

Angular velocity

There are two categories of the angular velocity: Spin angular velocity and orbital angular velocity. The spin angular velocity refers to the speed of rotation of an object or rigid body, with respect to its axis of rotation. The spin velocity of the angular object is independent of choice of origin, in contrast to the theory for orbital angular velocity.

In kinematics, we have studied the motion through a straight line and the concept of velocity or displacement and acceleration. In 2D kinematics, we deal with the concept of motion within two dimensions. The projectile motion is the special scenario for the 2D kinematics where the object is projected in the air. This object is subjected to gravitational force and then it lands a distance away. Here we will cover some of the situations where an object doesn’t land but moves in the curved path. 

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 which are rad/s.

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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

Rotational angles

The rotational angle involves an object that rotates about its own axis at the time of some other axis – for instance, a compact disk or a CD rotates about its centre – then each point within the object starts following a path that has the circular arc. You can visualise it as a line from the CD’s centre to the edge of the CD. The angle of rotation is essentially representing the amount of rotation and it is considered analogous to linear distance. The angular velocity can be defined as the rate of change in the angle.  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

Types and explanation of different angular motion

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 that 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.

If you have a rotating frame of three unit vectors then the coordinates of all the three should have the same angular speed at each of the points. In such frames, each vector can be regarded as the moving particle having a constant scalar radius. The rotating frame always tends to appear within the context of rigid bodies and specialised custom tools have been developed for this. 

Hence article explained what is angular motion and angular velocity. Students will develop a basic understanding of angular velocity after going through the article.