CBSE Class 11 Physics System Of Particles And Rotational Motion Notes Set 01

SYSTEM OF PARTICLES AND ROTATIONAL MOTION

MAIN POINTS

1. A rigid body is one for which the distance between different particles of the body do not change, even though there is a force acting on it. 

2. A rigid body fixed at one point or along a line can have only rotational motion. A rigid body not fixed in some way can have either pure rotation or a combination of translation and rotation. 

3. In pure translation every particle of the body moves with the same velocity at any instant of time.

4. In rotation about a fixed axis, every particle of the rigid body moves in a circle which lies in a plane perpendicular to the axis and has its centre on the axis. Every point in the rotating rigid body has the same angular velocity at any instant of time. 

5. Angular velocity is a vector. Its magnitude is ω = dѲ/dt and it is directed along the axis of rotation. For rotation about a fixed axis, this vector ω has a direction.

6. The vector or a cross product of two vectors A and B is a vector written as A X B. The magnitude of this vector is AB sin Ѳ and its direction is given by right handed screw or the right hand rule.

7. The linear velocity of a particle of rigid body rotating about a fixed axis is given by
v = ω x r wherre r is the position vector of the particle with respect to an origin along the fixed axis. The relation applies even to more general rotation of a rigid body with one point fixed. In that case r is the position vector of the particle with respect to the fixed point taken as the origin.

8. The centre of mass of the system particles is defined as the point whose position vector Is R= (Σmiri )/M

9. Velocity of the centre of mass of a system of particles is given by V = p/M, where P is the linear momentum of the system. The centre of mass moves as if all the mass of the system is concentrated at this point and all the external forces act at it .If the total external force is zero, then the total linear momentum of the system is constant.

10. The angular momentum of a system of n particles about the origin is
  
11. The Torque or moment of force on a system of n particles about the origin is given by

i=1  The force Fi acting on the ithparticle includes the external as well as the internal forces. Assuming Newton’s third law and that forces between any two particles act along the line joining the particles, we can show that Ƭint = 0 and dL/dt = Ƭext.

12. A rigid body is in mechanical equilibrium if

(i)It is I n translational equilibrium, i.e.’ the total external force on it is zero: ΣF_i =0and

(ii) It is in rotational equilibrium, i.e., the total external torque on it is zero: Σ τ_i= Σr_i x F _i = 0

13. The centre of gravity of an extended body is that point where the total gravitational torque on the body is zero.

14. The moment of inertia of a rigid body is defined by the formula I = Σ mi ri² Where ri Is the perpendicular distance of the ith point of the body from the axis. The kinetic energy of rotation is K = ½ I ω²

15. The theorem of parallel axes :I’= I_G + M a² where IG moment of inertia bout the axis passing through centre of gravity.

Allows us to determine the moment of inertia of a rigid body about an axis as the sum of the moment of inertia of the rigid body about a parallel axis passing through its center of mass and the product of its mass and the square of the perpendicular distance between the two parallel axes.

16. Rotation about a fixed axis is directly analogous to linear motion in respect of kinematics and dynamics.

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