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ramyani

Rotational Motion

JEE X-rayed.

The most important and most conceptual part of mechanics is the rotational motion of a body. This unit always remains one of the favorite topics of JEE paper-setters. Every year directly or indirectly questions have been asked from this unit carrying a good weightage.

The following are the points on which JEE people emphasize more and more:

Direction of frictional force in pure rolling motion (2 questions have been asked already)

Angular momentum of a moving particle or rotating body about some fixed point

(2 questions have been asked)

Conservation of angular momentum. (Many times)

Angular impulse

Conservation of energy principle

Collision of a body with another body

Pure rolling and impure rolling motion

JEE analysis table:

Year	Nature and description of questions	Concerned topic	Concepts and remarks
2007	1. Linked comprehension type
	Two discs ( having known MI have been imparted some angular velocity and kept in contact to acquire common angular velocity; to determine average torque in a time interval, loss in energy etc.	Work, energy, power Conservation of angular momentum Conservation of energy Calculation of torque	Kx ² / 2= Iw² / 2 To compute average frictional torque using integration i,e, for computation of torque due to distributed force, we have to employ integration Loss of energy = K_i - K_f
	2.Straight objective type I
	A small object is rolling on a curved surface and reaches upto a given maximum height; to determine the nature of object.	Pure rolling motion and conservation of energy	On a rough inclined or curved surface, the motion of purely rolling body remains pure rolling only, while on smooth surface it becomes impure rolling provided no other force is acting except gravitational and contact force.

2006	1. Straight objective type I
	A solid sphere is casted into a disc. Some info. abt mass, MI etc was given; to find radius of disc	MI	I for solid sphere abt dia = (2/5) MR² I ( disc ) abt its own axis = MR² /2 I = I (cm) + Md² ( parallel axis th.)
	2. Straight objective type I
	A ball moves on a fixed track, a part of which is rough and the other is smooth; to find the relation between weight on rough and smooth tracks and energies at various points.	Rolling motion Energy conservation	On a rough inclined or curved surface, the motion of purely rolling body remains pure rolling only, while on smooth surface it becomes impure rolling provided no other force is acting except gravitational and contact force.
	3. Straight objective type II
	A solid sphere is rolling without slipping down on an inclined plane. Options were given concerned with magnitude of friction force, work done by friction force, effect of friction on linear and angular velocity, dependence of friction force on inclination angle theta.	Pure rolling motion on an inclined plane	In pure rolling motion, the friction is static in nature, its value can be anyrhing between 0 to uN ( u = coeff. of friction ) Work done by friction force in pure rolling is zero, as point of contact is instantaneously at rest in pure rolling. Direction of frictional force decides the effect of linear and angular velocities.

2005	1. Straight objective type I
	A particle moves in a circular path with decreasing speed. Options are concerned with direction and magnitude of angular momentum, direction of accln and particle?s path.	Non-uniform circular motion. Dynamics of non-uniform circular motion.	Non-uniform circular motion means in addition to radial force, tangential force is also acting. If Torque = 0, then L = const. L = m r x v
	2. Straight objective type I	MI	I (remaining )= I ( full ) - I (removed )
	3. Analytical problem
	A bullet strikes a hanging rod and embedded into it; to determine average velocity of system just after impact.	Collision of a particle with a rigid body.	About pivotal, the angular momentum of the system just before collision = just after collision.
	4. Analytical problem
	A solid cylinder performs pure rolling on an inclined plane; to find its linear accln.	Pure rolling on an inclined plane.	Using basic concepts of pure rolling motion.

2004	1. Straight objective type I
	A disc is performing pure rolling on a horizontal surface; to find the relation between speeds of 3 specified points on the disc.	Kinematics of rotational motion.	V = sq.rt [ ( rw )² + v² ]
	2. Straight objective type I
	A child is standing with folded hands at the centre of rotating platform. If he stretches his hands, then what would be the new KE ?	Conservation of angular momentum.	I ₁w₁ = I ₂ w₂ KE = ( 1 / 2 ) Iw²

source : Physics spectrum , Dec 2007. My effort lies in typing.

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