Express angular momentum in terms of Rectangular Components of Linear Momentum and Position Vectors.
PHYSICS
CLASS 11
CH 7 SYSTEM OF PARTICLES AND ROTATIONAL MOTION
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Answer:
Now, moment of momentum is momentum vector mv=p multiplied by perpendicular distance from the reference point w.r.t. which the angular momentum is to be found. Generally, in practical calculations we choose a coordinate system and take it’s origin as reference point. So we have to take perpendicular distance of linear momentum from the origin of the chosen coordinate system. Now if vector r is position vector of the particle at some instant of time , there will be some angle ,say, (theta) between p and r. In this case |r|Sin(theta) will be perpendicular distance of p from the origin. Therefore, according to above definition, the angular momentum of the particle w. r. t. the chosen reference point will be |r||p|Sin(theta). This expression immediately reminds us of cross product of vector r and vector p.
Therefore, angular momentum is a vector given by l=rXp=mrXv.
The direction of l is perpendicular to the plane formed by r and p determined by right hand screw law.
Remember(1) angular momentum of a particle depends on the origin and hence on the position vector. If we change the origin angular momentum will also change. For example, if we take origin on the line of vector p then angular momentum will be zero. Therefore , while quoting angular momentum it is necessary to mention the reference point.
(2)Even a particle moving on a straight line can have angular momentum if origin or reference point is NOT falling on the straight line along which the particle moves.
(3)Kepler’s second law of planetary motion is nothing but law of conservation of angular momentum in case of central inverse square law of force.
(4) A rigid body rotating about an axis has angular momentum given by L=Iw,where I is moment of inertia of the body about the axis of rotation and w is angular velocity of the body about the axis.
Explanation:
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