Podcast
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?
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?
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
- v
- 0
- 2v (correct)
What is the total kinetic energy of a solid sphere of mass 1 kg rolling with a velocity of 1 m/s?
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?
Which mathematical relationship describes the graph between angular momentum and rotational kinetic energy of a rigid body about a given axis?
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?
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?
When a disk rolls without slipping, how does the linear velocity of its center of mass relate to the angular velocity?
When a disk rolls without slipping, how does the linear velocity of its center of mass relate to the angular velocity?
What is the consequence of reducing the moment of inertia of a rotating body on its angular momentum?
What is the consequence of reducing the moment of inertia of a rotating body on its angular momentum?
What shape represents the relationship between rotational kinetic energy and moment of inertia for a rigid body?
What shape represents the relationship between rotational kinetic energy and moment of inertia for a rigid body?
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?
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?
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?
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?
When a body is moving in a circular path with decreasing speed, what can be inferred about its angular momentum?
When a body is moving in a circular path with decreasing speed, what can be inferred about its angular momentum?
Which of the following describes the moment of inertia for three thin identical rods connected to form a specific shape?
Which of the following describes the moment of inertia for three thin identical rods connected to form a specific shape?
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?
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?
In a perfectly elastic collision where the initial velocity is not along the line connecting the centers, what scenario may occur?
In a perfectly elastic collision where the initial velocity is not along the line connecting the centers, what scenario may occur?
What is the effect of angular speed on the kinetic energy of a rolling solid sphere?
What is the effect of angular speed on the kinetic energy of a rolling solid sphere?
When does angular momentum of a body in circular motion become zero?
When does angular momentum of a body in circular motion become zero?
What will remain unchanged if the mass of the sun and earth is suddenly reduced to half, but the orbit remains the same?
What will remain unchanged if the mass of the sun and earth is suddenly reduced to half, but the orbit remains the same?
Which statement about the path followed by the center of mass of a disturbed vertically held rod is correct?
Which statement about the path followed by the center of mass of a disturbed vertically held rod is correct?
If two masses m and 2m revolve due to their mutual attraction, what is the ratio of their angular velocities?
If two masses m and 2m revolve due to their mutual attraction, what is the ratio of their angular velocities?
Which of the following cannot be zero for a particle moving on a circular path?
Which of the following cannot be zero for a particle moving on a circular path?
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?
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?
What happens to the rotation speed of the earth about its axis if the mass is halved?
What happens to the rotation speed of the earth about its axis if the mass is halved?
Which of the following describes an incorrect property of angular velocity, linear velocity, angular acceleration, and linear acceleration?
Which of the following describes an incorrect property of angular velocity, linear velocity, angular acceleration, and linear acceleration?
For a particle moving in a circle, which of the following can angular velocity be considered?
For a particle moving in a circle, which of the following can angular velocity be considered?
Which statement about the moment of inertia I concerning mass M and radius R is correct?
Which statement about the moment of inertia I concerning mass M and radius R is correct?
Which of the following is an axial vector?
Which of the following is an axial vector?
What type of quantities are angular velocity and angular momentum?
What type of quantities are angular velocity and angular momentum?
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?
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?
In the case of rolling with backward slipping friction, which of the following is true?
In the case of rolling with backward slipping friction, which of the following is true?
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?
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?
Which of these representations best describe the nature of rotational motion under rolling conditions?
Which of these representations best describe the nature of rotational motion under rolling conditions?
What will happen to a disc moving on an inclined plane when set into pure rolling?
What will happen to a disc moving on an inclined plane when set into pure rolling?
What happens to the angular speed of a wheel when a stationary particle is picked up at its edge?
What happens to the angular speed of a wheel when a stationary particle is picked up at its edge?
What is the moment of inertia of a wheel with radius R?
What is the moment of inertia of a wheel with radius R?
How does acceleration relate to velocity when an object is moving at constant speed?
How does acceleration relate to velocity when an object is moving at constant speed?
What will be the center of mass of a uniform circular plate of radius 2R with a disk of radius R removed?
What will be the center of mass of a uniform circular plate of radius 2R with a disk of radius R removed?
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?
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?
In rotational motion, what effect does adding mass to the edge of a rotating wheel have?
In rotational motion, what effect does adding mass to the edge of a rotating wheel have?
What is the relationship between linear acceleration and velocity in circular motion?
What is the relationship between linear acceleration and velocity in circular motion?
In a system of three identical cubes touching each other, how would the center of mass be located?
In a system of three identical cubes touching each other, how would the center of mass be located?
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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/3Ï€, 4R/3Ï€).
- 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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