Physics System of Particles and Rotational Motion

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Questions and Answers

What happens to the angular speed of a disc when a boy pulls his arms inward and reduces his moment of inertia by a factor of 2?

Remains the same

Becomes half of its initial value

Increases by a factor of four

Becomes double its initial value (correct)

What is the speed of a particle P located at the circumference of a disc that rolls without slipping with a center of mass velocity v?

v/2

2v (correct)

What is the total kinetic energy of a solid sphere of mass 1 kg rolling with a velocity of 1 m/s?

0.5 J

1.5 J

1 J (correct)

2 J

Which mathematical relationship describes the graph between angular momentum and rotational kinetic energy of a rigid body about a given axis?

Parabola Signup and view all the answers

If the moment of inertia of the boy is I0, what is the new moment of inertia of the disc after he pulls his arms in?

I0/2 Signup and view all the answers

When a disk rolls without slipping, how does the linear velocity of its center of mass relate to the angular velocity?

v = Rω Signup and view all the answers

What is the consequence of reducing the moment of inertia of a rotating body on its angular momentum?

Increases angular momentum Signup and view all the answers

What shape represents the relationship between rotational kinetic energy and moment of inertia for a rigid body?

Quadratic Signup and view all the answers

What is the relationship between the masses of two particles if one moving with velocity hits a sphere at rest elastically, and their final velocities are normal to each other?

2m1 = m2 Signup and view all the answers

If a solid sphere of mass M is rolling with angular speed on a horizontal plane, how is its angular momentum about point O expressed?

$\frac{2}{5} M R^2 \omega$ Signup and view all the answers

When a body is moving in a circular path with decreasing speed, what can be inferred about its angular momentum?

It decreases. Signup and view all the answers

Which of the following describes the moment of inertia for three thin identical rods connected to form a specific shape?

Depends on the configuration Signup and view all the answers

In the case where two particles of mass 2 kg and 4 kg are projected simultaneously from a height, which factor primarily affects their trajectory?

Initial velocity Signup and view all the answers

In a perfectly elastic collision where the initial velocity is not along the line connecting the centers, what scenario may occur?

One particle moves at right angles to the other. Signup and view all the answers

What is the effect of angular speed on the kinetic energy of a rolling solid sphere?

It increases with the square of angular speed. Signup and view all the answers

When does angular momentum of a body in circular motion become zero?

When it stops moving. Signup and view all the answers

What will remain unchanged if the mass of the sun and earth is suddenly reduced to half, but the orbit remains the same?

Angular momentum Signup and view all the answers

Which statement about the path followed by the center of mass of a disturbed vertically held rod is correct?

Straight line Signup and view all the answers

If two masses m and 2m revolve due to their mutual attraction, what is the ratio of their angular velocities?

1 : 1 Signup and view all the answers

Which of the following cannot be zero for a particle moving on a circular path?

Angular velocity Signup and view all the answers

When two point masses 6 kg and 3 kg are fixed at two ends of a rod of length 2 m, what is the moment of inertia about the center of mass?

4.5 kg·m² Signup and view all the answers

What happens to the rotation speed of the earth about its axis if the mass is halved?

It remains unchanged Signup and view all the answers

Which of the following describes an incorrect property of angular velocity, linear velocity, angular acceleration, and linear acceleration?

Must all be zero Signup and view all the answers

For a particle moving in a circle, which of the following can angular velocity be considered?

Can be non-negative Signup and view all the answers

Which statement about the moment of inertia I concerning mass M and radius R is correct?

I = MR^2 Signup and view all the answers

Which of the following is an axial vector?

Angular momentum Signup and view all the answers

What type of quantities are angular velocity and angular momentum?

Both are axial vectors Signup and view all the answers

In the scenario of a disc thrown upwards with a given angular motion, what will be true about the velocity of its center of mass after a certain time?

It becomes equal and opposite to the initial velocity Signup and view all the answers

In the case of rolling with backward slipping friction, which of the following is true?

Friction supports both rotational and translational motion Signup and view all the answers

At what point during the upward throw of the rotating disc will its center of mass velocity be equal and opposite to its initial velocity?

It can be either less or greater than 4 seconds Signup and view all the answers

Which of these representations best describe the nature of rotational motion under rolling conditions?

Rolling without slipping is always supported by friction Signup and view all the answers

What will happen to a disc moving on an inclined plane when set into pure rolling?

It accelerates downhill Signup and view all the answers

What happens to the angular speed of a wheel when a stationary particle is picked up at its edge?

The angular speed decreases. Signup and view all the answers

What is the moment of inertia of a wheel with radius R?

Dependent on the mass distribution and radius. Signup and view all the answers

How does acceleration relate to velocity when an object is moving at constant speed?

Acceleration is zero. Signup and view all the answers

What will be the center of mass of a uniform circular plate of radius 2R with a disk of radius R removed?

Shifted towards the removed disk. Signup and view all the answers

If a force is acting at a point given in coordinates (2 m, –3 m, 6 m), how can one determine the torque about a specified point?

By taking the cross product of the force and the position vector. Signup and view all the answers

In rotational motion, what effect does adding mass to the edge of a rotating wheel have?

Affects the moment of inertia and angular speed. Signup and view all the answers

What is the relationship between linear acceleration and velocity in circular motion?

Linear acceleration can exist even when velocity is constant. Signup and view all the answers

In a system of three identical cubes touching each other, how would the center of mass be located?

At the geometric center of the triangle formed by their centers. Signup and view all the answers

Study Notes

System of Particles and Rotational Motion

A body moving in a circular path with decreasing speed experiences a centripetal acceleration and a tangential acceleration in opposite directions.
In an elastic collision between a moving particle and a stationary sphere where their final velocities are normal to each other, the mass of the particle must be much greater than the mass of the sphere (m1 >> m2).
The moment of inertia of three identical rods of mass 'M' and length 'L' connected to form a shape (as shown in the figure), about an axis YY is 4ML²/3.
A solid sphere of mass M and radius R rolling on a horizontal plane with angular speed ω has an angular momentum of 7/5 MR²ω about the origin O.
Two particles of mass 2 kg and 4 kg projected from a tower simultaneously with different velocities will have their angular momentum conserved about the point of projection.
A disc rolling on ground without slipping has a velocity of v at its centre of mass, the speed of a particle P at the circumference (vp) is 2v.
The total kinetic energy of a solid sphere of mass 1 kg rolling with velocity 1 m/s is 7/10 J.
A disc rolling on an inclined plane, the speed of the point P at the circumference is the sum of the speed of the centre of mass and the speed due to the rotational motion.
The angular momentum and the rotational kinetic energy of a rigid body about a given axis are proportional to each other, forming a straight line when graphed.
Angular momentum, torque, and angular velocity are all axial vectors.
A rotating disc thrown upwards will take less than 4 seconds for its velocity of the centre of mass to become equal and opposite to the initial velocity (neglecting air friction and assuming g = 10 m/s²).
For two rotating objects, if the masses m and 2m are at a distance r and revolve due to their mutual attraction, the ratio of their angular velocities and the linear velocities is 1 : 1, 1 : 1.
If the mass of the sun and earth suddenly reduced to half and the orbit remains the same, the angular velocity of earth about the sun will change.
If the moment of inertia of a rotating body is reduced by a factor of 'm' and its angular speed doubles, the moment of inertia of the body will decrease by a factor of 'm'.
A wheel of moment of inertia I, radius R, and angular speed ω picks up a stationary particle of mass m at its edge, the new angular speed of the system will be ωI/(I + mR²).
If a rod held vertically on a smooth horizontal surface is slightly disturbed, the centre of mass of the rod will follow a parabolic path.
The centre of mass for a quarter ring of radius R placed as shown in the figure is (4R/3π, 4R/3π).
The moment of inertia of a system of two point masses (6 kg and 3 kg) fixed at the ends of a light rigid rod of length 2 m about the centre of mass and perpendicular to the rod is 9 kg m².

Additional Notes

This section focuses on rotational motion and the concepts related to it, including angular momentum, torque, and moment of inertia.
The text explores scenarios involving rotating bodies and their motion, focusing on the application of these concepts in various situations.
The text emphasizes the importance of conservation of angular momentum and how it affects the motion of rotating systems.
The questions provided in the text serve as practice problems for understanding the concepts and applying them to different situations.

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Description

Test your knowledge on the principles of rotational motion and the dynamics of particles in circular motion. This quiz covers concepts such as centripetal and tangential acceleration, moment of inertia, angular momentum, and collision scenarios. Perfect for students studying physics at an advanced level.