[PDF] SUBJECT- PHYSICS Angular velocity is the angle





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SUBJECT- PHYSICS

Angular velocity is the angle described by a rotating body per unit time. Angular acceleration is measured in radian sec-2.



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POWER SYSTEM STABILITY

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SYSTEM OF PARTICLES AND ROTATIONAL

MOTION

SUBJECT: PHYSICS

CLASS: XI

MODULE 1 OF 3

Module 1 of 3

System of Particles and Rotational Motion

equationsofmotionforrotationalmotion.

AngularVelocity;ʘͿ

willbe, ݐIf the particle describes one complete revolution then, The angular velocity is measured in radian second-1.

Its dimensional formula is [T-1].

Uniform Angular Velocity

If the particle describes equal angles in equal intervals of time then the angular velocity is said to be uniform. Angular acceleration is the rate of change of angular velocity with time. Here, n2and n1 are the number of revolutions made by the particle in one second.

Angular acceleration is measured in radian sec-2.

Its dimensional formula is [T-2].

Equations of Motion for Rotational Motion

For translatory motion, the equations of motion are as follows,

For rotational motion, the equations of motion are analogous to that for translatory motion. These are,

Mathematical Derivation of the First Equation of Motion for Rotational Motion Let ɘ଴be the initial angular velocity and ɘbe the final angular velocity after time t. This equation is known as the first equation of motion for rotational motion.

It describes therelation between initial angular velocity, final angular velocity and angular acceleration.

Mathematical Derivation of the Second Equation of Motion for Rotational Motion For translatorymotion, the displacement is given as, Similarly for rotational motion, the angular displacement is given as, From the first equation of motion for rotational motion we have,

Thus on substituting we get,

This equation is known as the second equation of motion for rotational motion.

It describes the relation between initial angular displacement, angular velocity, angular acceleration and time taken.

Mathematical Derivation of the Third Equation of Motion for Rotational Motion For rotational motion, the angular displacement is given as,

We know that,

ݐHence,

ɲTherefore,

This equation is known as the third equation of motion for rotational motion.

It describes the relation between initial angular velocity, final angular velocity, angular acceleration and angular

displacement. We shall now discuss some problems based on these equations of motion.

Problem 1

A wheel starts rotating at 10 rad s-1and attains anangular velocity of 100 rads-1in 15 s. What is the angular

acceleration in rad sec-2? (a) 10 rad s-2(b) ଵଵ଴ ଵହrad s-2(c) ଵ଴଴ ଵହrads-2(d) 6 rad s-2 ଵହൌ͸rad s-2

Problem 2

A wheel starts rotating from rest and attains an angular velocity of 60 rad s-1in 5 s. The total angular displacement in

radian will be (a) 60 rad(b) 80 rad(c) 100 rad(d) 150 rad

Solution:߱

Angular acceleration, ɲൌனିఠబ ହൌ12 rad s-2 Angular displacement, ԕൌɘ଴ݐ൅ଵ

Problem 3

A wheel having a diameter of 3 m starts from rest and accelerates uniformly to an angular velocity of 210 rpmin 5 s.

The angular acceleration of the wheel is

Solution:߱

But,

Thusangular acceleration is given as,

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