Angular Motion: Definition of Angular Motion, Relationship between Linear and Angular Motion (For CBSE, ICSE, IAS, NET, NRA 2022)

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In Physics, just as there are formulas to calculate linear velocity and displacement, there are also equivalent formulas to calculate angular movement.

Definition of Angular Motion

  • Angular motion is defined as, the motion of a body about a fixed point or fixed axis. It is equal to the angle passed over at the point or axis by a line drawn to the body.
  • Objects don՚t always travel in straight lines. For situations involving circular motion, such as the pendulum of a clock, or a door swinging, it՚s often easier to solve problems by looking at the angular motion of the objects.

Relationship between Linear and Angular Motion

  • Displacement – In linear motion, we use ′ x to quantify the linear distance travelled. In angular motion, we use ′ θ for the same to quantify the angular distance, and it is measured in radians.
  • Velocity – In linear motion, we use v to denote velocity while in angular motion, we use ′ ω to indicate angular velocity. Angular velocity is the number of radians covered per second.
  • Acceleration – We use ′ a to denote linear acceleration, while we use ′ α to mean the angular acceleration. The unit for angular acceleration is radians per second square.
  • Momentum: In linear motion, we use p to denote momentum while in angular motion, we use ′ L to indicate angular velocity.
  • Kinetic energy: In linear motion, we use ′ K ′ to denote momentum while in angular motion, we use ′ K to indicate angular velocity.
  • Force: In linear motion, we use F to denote momentum while in angular motion, we use ′ to indicate angular velocity.
  • Newton՚s second law of motion: In linear motion, we use F to denote momentum while in angular motion, we use ′ to indicate angular velocity.
  • Mass: In linear motion, we use ′ M ′ to denote momentum while in angular motion, we use ′ I ′ to indicate angular velocity

Table Shows a Relationship between Linear and Angular Motion

Relationship between Linear and Angular Motion
Linear motion termIn symbolsAngular motion termIn symbolsMagnitude of angular terms (if v, a and F are perpendicular to r the radius)
DisplacementAngular displacement
VelocityAngular velocity ​​
AccelerationAngular acceleration
Momentu​​mAngular momentum
Kinetic energyKinetic energy
ForceF​Torque (or moment)
Newton՚s Second Law of motionAngular version of Newton II
MassMMoment of inertia
  • One can work out angular equations of motion, like those for linear motion, provided the angular acceleration alpha, α is constant
  • For an object rotating about an axis, every point on the object has the same angular velocity.

What is an Angular Velocity?

The tangential velocity of any point is proportional to its distance from the axis of rotation. Angular velocity has the units rad/s.

  • Angular velocity , is the rate of change in angular displacement (radians per second) .

  • Angular velocity can also be given as the frequency of revolution, f (rev/s or rpm) :

Angular Velocity

Angular Velocity

Equation of Angular Versus Linear Velocity

Equation of Angular
AngularLinear
  • where is the angular speed at time t = 0
  • Δθ is the angular displacement.

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