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Rotation & Rigid Body Dynamics L3 | τ = I α , Pulleys with Mass, Rotational Energy | Class 11

Vedantu JEE English・76 minutes read

Captain Shreyas covers pulleys, torque, moment of inertia, and rotational kinetic energy, emphasizing key concepts while offering guidance and program updates. The lecture concludes with calculations of total kinetic energy, Earth's rotational kinetic energy, and angular speed of a falling rod, providing ample opportunity for further learning and practice.

Insights

Captain Shreyas is the lead lecturer, demonstrating a strong commitment to teaching and physics, engaging viewers and offering guidance on accessing educational resources.
The lecture emphasizes the crucial relationship between torque and moment of inertia, with torque being the cause and moment of inertia influencing the effect of angular acceleration, highlighting key concepts and formulas.
The importance of micro courses for concept clarity is underscored, offering live or recorded sessions as knowledge hubs, simplifying complex calculations and enhancing understanding in physics.

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Recent questions

What is the relationship between torque and moment of inertia?
Torque causes angular acceleration, moment of inertia influences it.
How can one simplify calculations involving pulleys and masses?
Use the trick of greater force minus opposing force divided by total mass.
What is the formula for calculating total kinetic energy of a rotating body?
Total kinetic energy is half the sum of mass times velocity squared for each particle.
How is the Earth's total rotational kinetic energy estimated?
Earth's rotational kinetic energy is approximately 2.3 x 10^32 joules.
How is the angular speed of a falling rod just before hitting the ground calculated?
The angular speed is the square root of 3g/l, where g is acceleration due to gravity and l is the length of the rod.

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Summary

00:00

Physics Lecture: Pulleys, Torque, and Kinetic Energy

Pulleys are discussed in relation to Newton's laws of motion, focusing on non-ideal pulleys with mass.
The lecture covers the essential equation linking torque and moment of inertia, concluding with rotational kinetic energy.
Captain Shreyas leads the lecture, welcoming viewers and emphasizing his passion for teaching and physics.
Viewers are encouraged to subscribe and like the channel, with special programs available for 11th standard students.
Various courses, crash courses, micro courses, and revision sessions are highlighted for students with backlogs or seeking additional help.
A Children's Day offer is mentioned, providing a 50% discount on Vedantu Pro subscriptions for 15 days.
Captain Shreyas interacts with viewers, addressing queries and offering guidance on accessing micro courses.
Recap on angular acceleration, moment of inertia, and torque is provided, emphasizing key concepts and formulas.
The relationship between torque and moment of inertia is explained, with torque being the cause and moment of inertia influencing the effect of angular acceleration.
The equation for net external torque on a body is revealed as the product of moment of inertia and angular acceleration, highlighting the crucial relationship between the two.

16:02

"Physics Concepts: Moment of Inertia Comparison"

Join the Telegram channel for daily updates, notifications, offers, and PDFs of homework solutions.
Class timing changed from 7:30 to 5:30 for the day due to other commitments.
Comparison of angular speeds between a solid sphere and a cylinder with the same mass and radius.
Moment of inertia of a cylinder is 1/2 * m * r^2, while for a solid sphere, it is 2/5 * m * r^2.
Cylinder's moment of inertia is greater than the solid sphere's, resulting in a lower angular speed for the cylinder.
Importance of micro courses for concept clarity, whether live or recorded, as a knowledge hub.
Calculation of moment of inertia for a wheel using torque, alpha, and time.
Conversion of RPM to radians per second for angular velocity calculations.
Determination of force required to bring a rotating wheel to rest in ten revolutions.
Impact of pulley mass on system acceleration, with mass leading to lower acceleration due to energy spent in pulley rotation.

32:49

Pulley Tension and Acceleration Simplified

The tension on a pulley is influenced by forces from the roof and the masses on either side.
The pulley's angular acceleration is determined by the net torque acting on it.
Torque is created by tension, not forces passing through the axis of rotation.
Tensions on both sides of the pulley must be different for angular acceleration to occur.
Equations for the pulley involve the torques created by the tensions on each side.
The ratio of tensions on the pulley's sides can be found by considering the forces and accelerations involved.
A trick to simplify calculations involves using the greater force minus the opposing force divided by the total mass.
The equivalent rotational mass for different pulley types simplifies calculations further.
Applying the trick to a system with multiple pulleys and masses can significantly reduce the complexity of solving equations.
By utilizing the trick, the acceleration and tension ratios in complex systems can be determined efficiently.

49:43

"Masses, Inertia, Torque, Tension: Physics Analysis"

Translating masses: 3m plus m are the translating masses, with the pulleys having a mass of 2m.
Moment of inertia calculation: Moment of inertia is mass times r square divided by 2, with the equivalent mass being m.
Equivalent mass determination: The equivalent mass for the pulley is m, as each pulley has the same mass.
Mass calculation: 3m minus m equals 2m, leading to 2mg divided by 6.
Newton's law equation: Net force equals mass times acceleration, with the only forces being tension and weight.
Torque calculation: Taking torque about the center, applying a pseudo force due to acceleration, and finding the torque due to the 2t force.
Torque analysis: Torque due to pseudo force and gravity is zero, with only the torque from the 2t force contributing to the alpha.
Tension calculation: Tension is found to be mg divided by 6.
Rod suspension scenario: A rod suspended by two strings, with one string being cut, leading to the rod tilting and the question of tension in the remaining string.
Equations setup: Using Newton's laws and rotational equations to determine the tension in the remaining string, considering the relationship between acceleration and angular acceleration.
Final tension calculation: Tension in the remaining string is found to be mg divided by 4.

01:06:37

Rotational Kinetic Energy Formulas and Calculations

Different particles with varying masses have different distances and speeds due to their velocity v2.
Each particle's speed, such as v1, v2, x7, is calculated as omega multiplied by r1 or r2.
The total kinetic energy of a rotating body is the sum of kinetic energies of all particles.
The formula for total kinetic energy is the sum of half the mass times the velocity squared for each particle.
The formula for rotational kinetic energy is derived as half omega squared times the moment of inertia.
The formula for rotational energy, half I omega squared, is easy to remember due to its similarity to kinetic energy of translation.
The Earth's total rotational kinetic energy is estimated using the formula for a solid sphere's moment of inertia.
The Earth's rotational kinetic energy is calculated to be approximately 2.3 x 10^32 joules.
The work done by torque in changing the kinetic energy of a rotating wheel is calculated using the formula half I omega final squared minus half I omega initial squared.
The angular speed of a falling rod just before hitting the ground is determined by converting gravitational potential energy into rotational kinetic energy.

01:23:41

Rod's Energy and Motion Calculations

The center of mass of a rod is located at a distance of l by 2 from one end.
The potential energy of the rod is calculated by finding the potential energy of the center of mass, which is mgh at l by 2.
The rotational kinetic energy of the rod is determined by half the moment of inertia of the rod multiplied by omega squared, resulting in mg l = I.
To find the moment of inertia about the end of the rod, the parallel axis theorem is used, resulting in I = ml^2/3.
The angular speed of the rod just before hitting the ground is calculated to be the square root of 3g/l.
Homework questions are provided for practice, with solutions to be posted in the comments section.

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