- Rotational Motion
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- Angular velocity
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- Angular acceleration
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- Rotation with constant angular acceleration
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- Kinetic energy of Rotation
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- Calculation of moment of inertia
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- Parallel Axis Theorem|Theorems of Moment of Inertia
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- Perpendicular Axis Theorem
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- Torque
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- work and power in rotational motion
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- Angular acceleration
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- Relationship between Angular momentum and torque
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- Conservation of Angular momentum
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- Radius of gyration
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- Rolling Motion|Kinetic Energy of rolling bodies
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- Rotational Motion problems with solutions

- Consider a rigid body of arbitrary shape rotating about a fixed axis through point O and perpendicular to the plane of the paper as shown below in the figure-1

- while the body is rotating each and every point in the body moves in a circle with their center lying on the axis of rotation and every point moves through the same angle during a particular interval of time

- Consider the position of a particle say i
^{th}particle at point P at a distance r_{i}from point O and at an angle θ_{i}which OP makes with some reference line fixed in space say OX as shown below in the figure

- If particle moves an small distance ds
_{i}along the arc of the circle in small amount of time dt then

ds_{i}=v_{i}dt ----(1)

where v_{i}is the speed of the particle - dθ is the angle subtended by an arc of length ds
_{i}on the circumference of a circle of radius r_{i},so dθ( in radians) would be equal to the length of the arc divided by the radius

i.e.

dθ=ds_{i}/r_{i}=v_{i}dt/r_{i}----(2) - distance ds
_{i}would vary from particle to particle but angle dθ swept out in a given time remain same for all the particles i.e. if particle at point P moves through complete circle such that

dθ=2π rad

Then all the other particles of the rigid body moves through the angular displacement dθ=2π

- So rate of change of angle w.r.t time i.e. dθ/dt is same for all particles of the rigid body and dθ/dt is known as angular velocity ω of the rigid body so

ω=dθ/dt ----(3) - Putting equation (3) in equation (2) we find

v_{i}=r_{i}(dθ/dt) =r_{i}ω ---(4)

This shows that velocity of ith particle of the rigid body is related to its radius and the angular velocity of the rigid body

- Angular velocity of a rotating rigid body can either be positive or negative. It is positive when the body is rotating in anticlockwise direction and negative when the body id rotating in clockwise direction

- Unit of angular velocity radian per second (rad-s
^{-1}) and since radian is dimensionless unit of angle so dimension of angular velocity is [T^{-1}] - Instead of radians angles are often expressed in degrees. So angular velocity can also be expressed in terms of degree per second and degree per minute
- we know that

2π radians =360^{0}

or π radians/180^{0}=1 And this relation can be used for expressing angular velocity in degree to that of angular velocity in terms of radian

Class 11 Maths Class 11 Physics Class 11 Chemistry

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