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12th PHYSICS | ROTATIONAL DYNAMICS | LECTURE 13 | NUMERICALS | PRADEEP GIRI SIR

Giri Tutorials・133 minutes read

The video explains numerical problems related to a bicycle wheel's rotation and guides viewers on calculations involving displacement and angular velocity. It covers topics like static friction, centrifugal force, and minimum speed calculations, emphasizing the importance of precision and accuracy in mathematical studies.

Insights

Emphasizing the time-consuming nature of numerical problems
Detailing the task of calculating the number of revolutions in 10 seconds
The concept of maximum velocity is discussed, particularly in relation to angles over 45°
The text stresses the importance of visualizing scenarios and understanding the concepts of potential energy

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Recent questions

How can I calculate the number of revolutions in 10 seconds?
By converting linear equations to angular equations.
What is the significance of balancing centrifugal force and static friction?
It determines the maximum speed and stability of motion.
How can I calculate the minimum speed for circular motion?
By determining the value of Tan Theta accurately.
What is the process for calculating potential energy changes?
By visualizing height differences and applying the potential energy formula.
How can I calculate the moment of inertia for different objects?
By applying specific formulas and the parallel axis theorem.

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Summary

00:00

"Mastering Numerical Problems with Bicycle Wheel"

Starting numerical lessons after completing the first lesson
Emphasizing the time-consuming nature of numerical problems
Encouraging practice and engagement with the content
Requesting viewers to subscribe, like, and share the video
Presenting a numerical question involving a bicycle wheel's rotation
Explaining the setup of the bicycle wheel on a central stand
Describing the angular acceleration and frequency of the wheel
Detailing the task of calculating the number of revolutions in 10 seconds
Introducing the need to determine the time taken for the first and last completed revolution
Providing guidance on converting linear equations to angular equations for solving the problem

15:00

Kinematic equations and motion with displacement

The text discusses kinematic equations and motion, focusing on displacement and angular velocity.
It mentions the change in displacement and the Android displacement θ.
The text delves into the concept of acceleration, specifically alpha t².
It emphasizes the value of alpha, which is 0.45.
The text explains the process of multiplying by 10 and the resulting calculations.
It introduces the concept of square roots and the unit of square root of 10.
The text transitions to discussing Roshan and the time taken for different scenarios.
It highlights the importance of log tables and their relevance in mathematical studies.
The text moves on to a practical example involving static friction and a gramophone disc.
It concludes with a numerical problem involving determining the minimum frequency for a coin to start slipping on the disc.

32:26

Calculating Forces and Frequencies in Physics

The text discusses input and output, focusing on the X Axis and a coin.
It delves into concepts like download force, normal reaction, and static friction.
The text mentions balancing centrifugal force and static friction.
It introduces equations involving omega and radius, emphasizing frequency.
The text involves calculations related to radius, distance, and frequency.
It emphasizes the importance of numerical accuracy and precision in calculations.
The text guides on finding the value of Omega and solving equations.
It discusses the process of dividing and simplifying numerical results.
The text transitions to a new topic involving a racing track design.
It concludes with instructions on finding the angle of banking and outer height in the racing track scenario.

51:36

"Dividing, angles, and speed limits explained"

The text provides a method for dividing 6 by 6, resulting in 36 divided by 2 equals 72.
It suggests dividing 2 by 10 to get 5, encouraging the reader to continue dividing as they know how.
The text mentions joining a class for fast and second standard students, involving a cricket wicket and division.
It instructs to find an angle by raising a ghost, locking a table, and observing natural tension.
A playlist is mentioned for further guidance, emphasizing the importance of searching for "tan inverse."
The text advises finding a number between 4 and 5, specifically focusing on the smallest number.
It explains the process of selecting the closest number, highlighting the importance of precision.
The text delves into finding the value of 78 degrees and 42 minutes, emphasizing the need for accuracy.
It discusses the concept of static friction and maximum speed, linking it to the angle of banking.
The text concludes by explaining the formula for maximum speed, highlighting the significance of angles and friction in determining speed limits.

01:07:08

Unlimited Speed: Calculations and Requirements

The maximum speed of the vehicle has no limit, allowing for infinite running.
There is no speed limit regardless of the speed increase.
The concept of maximum velocity is discussed, particularly in relation to angles over 45°.
The formula for minimum speed is detailed, emphasizing the importance of specific calculations.
The value of Tan Theta is crucial in determining the minimum speed.
The process of converting kilometers to meters per second is explained.
The minimum speed for running is calculated to be 88.52 km/h.
A stunt artist's minimum speed requirement for performing circular motion is discussed.
The force of friction needed to match the minimum speed is determined to be 500 Newtons.
The formula for finding the minimum velocity in a pendulum system is outlined.

01:23:32

Calculating Conical Pendulum Frequency and Energy

The length of the conical pendulum is 20 centimeters, with a bob inside weighing 100 grams.
The conical pendulum's bob performs at 75 rpm, requiring the calculation of its frequency.
To calculate the kinetic energy and increase in gravitational potential energy of the pendulum, a change in potential energy must be extracted.
The formula for kinetic energy is 1/2 * m * v^2, with the horizontal velocity of the conical pendulum needed for calculation.
The frequency of the conical pendulum is determined by the formula G/L * tan(theta).
The value of the frequency is 1.25, which is squared to find the frequency's square root.
The reciprocal of 0.8 is calculated by finding the closest number to 0.800, which is 36 degrees and 48 minutes.
The difference between the calculated value and the desired value of 800 is determined by subtracting, resulting in 36 degrees and 48 minutes.
To find the cosine of 36 degrees and 48 minutes, the value is subtracted from 8007, yielding the accurate result.
The final result is 36 degrees and 48 minutes, showcasing the precision of the calculation.

01:40:24

"Mastering Calculations: Potential Energy and More"

The text discusses calculations involving numbers like 87, 800, 0.8, 8007, 48, 36, 52, 0.599, 0.7481, 0.75, 0.045, and 0.05.
It mentions the need to write down whose mines were given to whom and emphasizes the importance of paying attention to specific numbers.
Instructions are given to perform calculations involving minutes, degrees, and plus operations.
The text highlights the significance of accurately determining values and the process of finding accurate answers.
It mentions the need to find the radius and provides steps to solve equations involving specific values like 100 * 10^-3.
Practical advice is given on using tables, logarithms, and antilogs for calculations.
The text discusses the process of finding kinetic and potential energy, emphasizing the importance of understanding differences in potential energy.
It provides a detailed explanation of the scenario involving a bob moving from one point to another and the calculation of potential energy based on height differences.
The text stresses the importance of visualizing scenarios and understanding the concepts of potential energy.
It concludes by encouraging readers to practice calculations and understand the intricacies of potential energy calculations.

01:57:47

Calculating Potential Energy Changes with Precision

The mug represents the general formula for potential energy, with its value being mg.
Bob's height is considered zero, leading to the potential energy being zero as well.
The change in potential energy is linked to the change in height, with the initial position being where Bob stopped first.
The potential energy formula is applied as Bob moves from one point to another, considering the height differences.
The calculation involves determining the potential energy at various points based on height comparisons.
The string's length is a crucial factor in the calculations, requiring precise measurements.
The process involves finding the value of variables like Ha and A, crucial for further calculations.
The calculation includes determining the potential energy change and its impact on the overall energy equation.
The practical application involves complex mathematical operations to derive the final potential energy value.
The entire process of calculating potential energy and its changes requires meticulous attention to detail and mathematical accuracy.

02:17:38

Moment of Inertia Calculations for Objects

Momentum inertia is based on the diameter of the ring, with a given value of 1 k.
The ring is melted and re-molded into a disk, with the mass of the ring being equal to the mass of the disk.
The radius of the disk is the same as the radius of the ring.
The moment of inertia of the disk is calculated using the formula mr²/2 when the axis passes through the center.
The formula for the moment of inertia of the ring is also mr²/2 when the axis passes through the diameter.
The moment of inertia of the dumbbell is calculated using the parallel axis theorem, with the axis passing through the center and perpendicular to the length.
The total moment of inertia of the dumbbell is found by adding the moment of inertia of the road and the sphere.
The radius of the sphere is given as 10 centimeters, and the total length of the road is 20 centimeters.
The distance between the parallel axes for the road and the sphere is calculated as 20 centimeters.
The moment of inertia of both spheres is the same due to their identical characteristics, resulting in a direct multiplication by 2 for the final value.

02:33:26

Solving Momentum and Mass Mathematical Problem

The text discusses solving a mathematical problem involving momentum and mass.
The formula for momentum is mentioned as 2/5M.
The mass of the road is stated to be 60.
The distance between two parallel axes is given as 10.
The radius is calculated to be 10.
The total distance between the two axes is determined to be 20.
The final answer is calculated to be 46 centimeter square.
The frequency of a disk is given as 100 RPM.
The mass of the disk is stated as 10 kg.
The new frequency after a clay mass falls on the disk is found to be 80 RPM.

02:54:09

Inclined surfaces, rolling bodies, and momentum calculations

The text discusses solving numerical problems related to inclined surfaces and rolling bodies.
It explains the process of finding the total distance covered by a traveler, which is 5/3 meters.
The text delves into calculating the velocity of a rolling body along an inclined surface using specific formulas and values.
It concludes by discussing momentum inertia and the completion of all numerical problems up to question 22.

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