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A circular disc of mass m and radius R is set into motion on a horizontal floor with a linear speed v in the forward direction and an angular speed omega=v/3R in clockwise direction. Find the magnitude of the total angular momentum of the disc about the axis perpendicular to the plane of disc and passing through the bottom most point 'O' of the disc and fixed to the ground.
Most Upvoted Answer
A circular disc of mass m and radius R is set into motion on a horizon...
Angular momentum of any body from any fixed point O is nothing but the sum of angular momentum of the centre of mass and angular momentum about centre of mass. In this question the Angular momentum of centre of mass is mvR and Angular momentum about center of mass is moment of inertia times Omega = mR^2 times v/3R = mvR/3
Therefore the total Angular momentum is mvr + mvr/3 = 4mvR/3
Therefore the total Angular momentum is mvr + mvr/3 = 4mvR/3
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A circular disc of mass m and radius R is set into motion on a horizon...
Problem:
A circular disc of mass m and radius R is set into motion on a horizontal floor with a linear speed v in the forward direction and an angular speed ω=v/3R in clockwise direction. Find the magnitude of the total angular momentum of the disc about the axis perpendicular to the plane of the disc and passing through the bottommost point 'O' of the disc and fixed to the ground.
Solution:
Step 1: Understanding the problem
To solve this problem, we need to calculate the magnitude of the total angular momentum of the disc about the axis passing through the bottommost point 'O' of the disc and perpendicular to the plane of the disc.
Step 2: Defining the variables
Let's define the given variables:
- m: mass of the disc
- R: radius of the disc
- v: linear speed of the disc
- ω: angular speed of the disc
Step 3: Understanding angular momentum
Angular momentum is a vector quantity that depends on both the mass and the distribution of mass in an object, as well as its velocity or angular velocity. The angular momentum of an object rotating about a fixed axis is given by the equation:
L = Iω
Where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity.
Step 4: Calculating the moment of inertia
The moment of inertia of a disc rotating about an axis perpendicular to its plane and passing through its center is given by the equation:
I = (1/2)mR^2
Step 5: Calculating the angular momentum
Substituting the values of moment of inertia and angular velocity into the equation for angular momentum, we get:
L = (1/2)mR^2 * (v/3R)
Simplifying the equation, we get:
L = (1/6)mv
Step 6: Final answer
The magnitude of the total angular momentum of the disc about the axis passing through the bottommost point 'O' of the disc and perpendicular to the plane of the disc is given by (1/6)mv.
A circular disc of mass m and radius R is set into motion on a horizontal floor with a linear speed v in the forward direction and an angular speed ω=v/3R in clockwise direction. Find the magnitude of the total angular momentum of the disc about the axis perpendicular to the plane of the disc and passing through the bottommost point 'O' of the disc and fixed to the ground.
Solution:
Step 1: Understanding the problem
To solve this problem, we need to calculate the magnitude of the total angular momentum of the disc about the axis passing through the bottommost point 'O' of the disc and perpendicular to the plane of the disc.
Step 2: Defining the variables
Let's define the given variables:
- m: mass of the disc
- R: radius of the disc
- v: linear speed of the disc
- ω: angular speed of the disc
Step 3: Understanding angular momentum
Angular momentum is a vector quantity that depends on both the mass and the distribution of mass in an object, as well as its velocity or angular velocity. The angular momentum of an object rotating about a fixed axis is given by the equation:
L = Iω
Where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity.
Step 4: Calculating the moment of inertia
The moment of inertia of a disc rotating about an axis perpendicular to its plane and passing through its center is given by the equation:
I = (1/2)mR^2
Step 5: Calculating the angular momentum
Substituting the values of moment of inertia and angular velocity into the equation for angular momentum, we get:
L = (1/2)mR^2 * (v/3R)
Simplifying the equation, we get:
L = (1/6)mv
Step 6: Final answer
The magnitude of the total angular momentum of the disc about the axis passing through the bottommost point 'O' of the disc and perpendicular to the plane of the disc is given by (1/6)mv.
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A circular disc of mass m and radius R is set into motion on a horizontal floor with a linear speed v in the forward direction and an angular speed omega=v/3R in clockwise direction. Find the magnitude of the total angular momentum of the disc about the axis perpendicular to the plane of disc and passing through the bottom most point 'O' of the disc and fixed to the ground.
Question Description
A circular disc of mass m and radius R is set into motion on a horizontal floor with a linear speed v in the forward direction and an angular speed omega=v/3R in clockwise direction. Find the magnitude of the total angular momentum of the disc about the axis perpendicular to the plane of disc and passing through the bottom most point 'O' of the disc and fixed to the ground. for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A circular disc of mass m and radius R is set into motion on a horizontal floor with a linear speed v in the forward direction and an angular speed omega=v/3R in clockwise direction. Find the magnitude of the total angular momentum of the disc about the axis perpendicular to the plane of disc and passing through the bottom most point 'O' of the disc and fixed to the ground. covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A circular disc of mass m and radius R is set into motion on a horizontal floor with a linear speed v in the forward direction and an angular speed omega=v/3R in clockwise direction. Find the magnitude of the total angular momentum of the disc about the axis perpendicular to the plane of disc and passing through the bottom most point 'O' of the disc and fixed to the ground..
A circular disc of mass m and radius R is set into motion on a horizontal floor with a linear speed v in the forward direction and an angular speed omega=v/3R in clockwise direction. Find the magnitude of the total angular momentum of the disc about the axis perpendicular to the plane of disc and passing through the bottom most point 'O' of the disc and fixed to the ground. for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A circular disc of mass m and radius R is set into motion on a horizontal floor with a linear speed v in the forward direction and an angular speed omega=v/3R in clockwise direction. Find the magnitude of the total angular momentum of the disc about the axis perpendicular to the plane of disc and passing through the bottom most point 'O' of the disc and fixed to the ground. covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A circular disc of mass m and radius R is set into motion on a horizontal floor with a linear speed v in the forward direction and an angular speed omega=v/3R in clockwise direction. Find the magnitude of the total angular momentum of the disc about the axis perpendicular to the plane of disc and passing through the bottom most point 'O' of the disc and fixed to the ground..
Solutions for A circular disc of mass m and radius R is set into motion on a horizontal floor with a linear speed v in the forward direction and an angular speed omega=v/3R in clockwise direction. Find the magnitude of the total angular momentum of the disc about the axis perpendicular to the plane of disc and passing through the bottom most point 'O' of the disc and fixed to the ground. in English & in Hindi are available as part of our courses for JEE.
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A circular disc of mass m and radius R is set into motion on a horizontal floor with a linear speed v in the forward direction and an angular speed omega=v/3R in clockwise direction. Find the magnitude of the total angular momentum of the disc about the axis perpendicular to the plane of disc and passing through the bottom most point 'O' of the disc and fixed to the ground., a detailed solution for A circular disc of mass m and radius R is set into motion on a horizontal floor with a linear speed v in the forward direction and an angular speed omega=v/3R in clockwise direction. Find the magnitude of the total angular momentum of the disc about the axis perpendicular to the plane of disc and passing through the bottom most point 'O' of the disc and fixed to the ground. has been provided alongside types of A circular disc of mass m and radius R is set into motion on a horizontal floor with a linear speed v in the forward direction and an angular speed omega=v/3R in clockwise direction. Find the magnitude of the total angular momentum of the disc about the axis perpendicular to the plane of disc and passing through the bottom most point 'O' of the disc and fixed to the ground. theory, EduRev gives you an
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