JEE-Main - Grade 11 - Physics - System of Particles and Rotational Motion - Importance and Snapshot of System Of Particles And Rotational Motion - Study ref# 710

Introduction:
Any real body which we encounter in daily life has a finite
size. In dealing with the motion of extended bodies (bodies of finite size)
often the idealized model of a particle is inadequate. In this chapter, we
shall try ... read more

JEE-Main - Grade 11 - Physics - System of Particles and Rotational Motion - Importance and Snapshot of System Of Particles And Rotational Motion - Study ref# 711

Following sections must be covered to understand System of
Particles and Rotational Motion:
1. Introduction
2. Center of mass
3. Motion of center of mass
4. Linear momentum of a system of particles
5. Vector products of two vecto... read more

JEE-Main - Grade 11 - Physics - System of Particles and Rotational Motion - Target Setup for System Of Particles And Rotational Motion - Study ref# 736

Student requires to achieve the following milestones to get better grip over System Of Particle And Rotational Motion. The milestones / targets are as follows:- Starting Point: Days 0Test TypeAppear on TestTarget TestsScorePracti... read more

JEE-Main - Grade 11 - Physics - System of Particles and Rotational Motion - Study ref# 398

What is the total linear momentum of a system of particles? Answer: The total linear momentum of a system of particles is equal to the product of total mass of the system and velocity of centre of mass. So, ... read more

JEE-Main - Grade 11 - Physics - System of Particles and Rotational Motion - Study ref# 400

What is the angular velocity of earth spinning around its own axis? Answer: The angular velocity of earth spinning around its own axis is... read more

JEE-Main - Grade 11 - Physics - System of Particles and Rotational Motion - Study ref# 401

The moment of inertia of a solid sphere about a tangent is . What would be its moment of inertia about its diameter? Answer: According to parallel axis theorem, ... read more

JEE-Main - Grade 11 - Physics - System of Particles and Rotational Motion - Study ref# 402

What is the radius of gyration of a solid sphere of mass m and radius R about its diameter? Answer: For solid sphere From the definition of radius of gyration, &n... read more

JEE-Main - Grade 11 - Physics - System of Particles and Rotational Motion - Study ref# 405

An isolated particle of mass m is moving in a horizontal (x-y) plane along x-axis at a certain height above the ground. It explodes suddenly into two fragments of masses . An instant later, the smaller fragment is at What is the posit... read more

JEE-Main - Grade 11 - Physics - System of Particles and Rotational Motion - Study ref# 406

A particle is moving along a straight line parallel to x-axis with constant velocity. How does the angular momentum of the particle change about the origin? Answer: Suppose a particle of mass m is moving with velocity v parallel to x-axis from B, whe... read more

JEE-Main - Grade 11 - Physics - System of Particles and Rotational Motion - Study ref# 407

Which one has larger angular velocity between rotation of hour hand of a watch and rotation of earth about its axis? Answer: The hour hand of a watch takes 12 hr to complete one rotation i.e. And the earth takes 24 hr to rotate about its a... read more

JEE-Main - Grade 11 - Physics - System of Particles and Rotational Motion - Study ref# 408

Find radius of gyration of a rod of length l and mass m about an axis perpendicular to its length and passing through one end. Answer: According to parallel axis theorem, Now, from the definition of radius of gyration, &nb... read more

JEE-Main - Grade 11 - Physics - System of Particles and Rotational Motion - Study ref# 409

The moments of inertia of two rotating bodies A and B are and and their angular momentum are equal. Which one has greater kinetic energy? Answer: We know, angular momentum And kinetic energy of rotation &nb... read more

JEE-Main - Grade 11 - Physics - System of Particles and Rotational Motion - Study ref# 410

Define radius of gyration. If moment of inertia of a solid sphere about its diameter is then find the radius of gyration about that axis. Answer: Radius of gyration: Radius of gyration of a body about a given axis is the perpendicu... read more

JEE-Main - Grade 11 - Physics - System of Particles and Rotational Motion - Study ref# 411

i) State parallel axis theorem of moment of inertia. ii) Find the moment of inertia of a ring of mass M and radius R about the axis tangent to that ring and resides in the plane of ring. Answer: i) Parallel axis theorem: ... read more

JEE-Main - Grade 11 - Physics - System of Particles and Rotational Motion - Study ref# 412

i) State perpendicular axis theorem of moment of inertia. ii) Find the moment of inertia of a circular disc of mass M and radius R about an axis passing through its centre and perpendicular to its plane. Given, moment o... read more

JEE-Main - Grade 11 - Physics - System of Particles and Rotational Motion - Study ref# 413

A uniform rod of length L has moment of inertia about an axis passing through the centre of mass is . Findi) Moment of inertia of that rod about an axis passing through one end of rod.ii) The radius of gyration of that rod about the axis in 1st&... read more

JEE-Main - Grade 11 - Physics - System of Particles and Rotational Motion - Study ref# 414

Show that, the total angular momentum of a rigid body of mass M about a given axis is equal to the product of moment of inertia of that rigid body about that axis and the angular velocity of it. Answer: Consider a rigid body of mass M is ro... read more

JEE-Main - Grade 11 - Physics - System of Particles and Rotational Motion - Study ref# 415

Write the principle of conservation of angular momentum. Derive this conservation principle from the relation between torque and angular momentum of a rigid body. Answer: Principle of conservation of angular momentum: when no external fo... read more

JEE-Main - Grade 11 - Physics - System of Particles and Rotational Motion - Study ref# 416

If no external torque is acting on a rigid body, angular momentum is conserved. Is the kinetic energy of rotation conserved or not? Answer: Suppose there is no external torque acting on a rigid body, then Consider But kinetic energy or rota... read more

JEE-Main - Grade 11 - Physics - System of Particles and Rotational Motion - Study ref# 417

A thin hollow cylinder, open at both ends and weighing 5 kg (a) slides with a speed of 10m/s without rotating (b) rolls with the same speed without slipping. Compare the kinetic energies of the cylinder in two cases. Answer: Given that, m = 5 kg, v =... read more

JEE-Main - Grade 11 - Physics - System of Particles and Rotational Motion - Study ref# 418

Three blocks of uniform thickness and masses m, m and 2m are placed at the corners of a triangle having co-ordinates and respectively. Find the co-ordinates of the centre of mass of the system. Answer: x co-ordinate of centre of mass ... read more

JEE-Main - Grade 11 - Physics - System of Particles and Rotational Motion - Study ref# 419

The radius of a wheel of car is 0.4 m. The car is accelerated from rest by an angular acceleration of 1.5 rad/s2 for 20 sec. How much distance will the wheel cover in this time and what will be its linear velocity? Answer: Here, radius r = 0.4 m,&nbs... read more

JEE-Main - Grade 11 - Physics - System of Particles and Rotational Motion - Study ref# 420

Show that the centre of mass of two particles of equal masses lies exactly midway between them. Answer: The centre of mass of two masses system is --------- (i)Now if the two masses are same then &n... read more

JEE-Main - Grade 11 - Physics - System of Particles and Rotational Motion - Study ref# 421

A wheel of moment of inertia 0.5 kg m2 and radius 20 cm is rotating about its axis at an angular speed of 20 rad/s. it picks up a stationary particle of mass 200 gm at its edge. Find the new angular speed of the wheel. Answer: Here When a partic... read more

JEE-Main - Grade 11 - Physics - System of Particles and Rotational Motion - Study ref# 422

Calculate the kinetic energy of rotation of a circular disc of mass 1 kg and radius 0.2 m rotating about an axis passing through its centre and perpendicular to its plane. The disc is completing rotations per minute. Answer: Here &nbs... read more

JEE-Main - Grade 11 - Physics - System of Particles and Rotational Motion - Study ref# 423

A body of mass 5 kg is attached to a weightless string wound round a circular disc of mass 8 kg and radius 0.3 m. the body is allowed to fall. Calculate (i) tension in the string, (ii) acceleration with which the body falls and (iii) angular accelera... read more

JEE-Main - Grade 11 - Physics - System of Particles and Rotational Motion - Study ref# 424

Show that the angular momentum about any point of a single particle moving with constant velocity remains constant throughout the motion. Answer: Suppose, at any time t, the particle at P is moving with velocity v. We have to calculate angu... read more

JEE-Main - Grade 11 - Physics - System of Particles and Rotational Motion - Study ref# 425

A person carrying dumbbells in his hands are outstretched and standing on a rotating table. He rotates faster when hands are taken inwards. Explain. Answer: Here no net external torque is acting on the system consisting of the person, dumbbells and r... read more

JEE-Main - Grade 11 - Physics - System of Particles and Rotational Motion - Study ref# 426

Can a body at translatory motion have angular momentum? Explain. Answer: Yes, a body in translatory motion shall have angular momentum. In this case, the fixed point about which angular momentum is taken will not lie on the line of motion of the body... read more

JEE-Main - Grade 11 - Physics - System of Particles and Rotational Motion - Study ref# 427

Show that, torque is equal to the rate of change of angular momentum of a rigid body. Answer: From Newtonâ€™s second law, we can write F = ------- (i)Where P is linear momentum of the rigid body. The vector ... read more