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A square plate of mass m and edge L is shown in the figure moment of intertia of the plate about the axis in the plane of plate and passing through one of its vertex making an angle 15° with its side
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A square plate of mass m and edge L is shown in the figure moment of i...
The moment of inertia of a uniform square plate about any axis passing through its center and lying in its plane is same and is equal to I.
in terms of mass and dimensions of the square plate the expression for I is
I = ML2/12
where M = mass of the plate
and L = side length
Tan15= perpendicular /L
= 1/2 (ML2 -ML2/12)
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A square plate of mass m and edge L is shown in the figure moment of i...
Calculation of Moment of Inertia of a Square Plate
1. Given Parameters:
- Mass of the plate, m
- Edge length of the square plate, L
- Angle between the axis and the plate's side, 15°
2. Moment of Inertia Formula:
- Moment of inertia (I) of a plate about an axis in its plane passing through one of its vertices can be calculated using the formula:
I = (m * L^2) / 3
3. Calculation with Angle:
- When the axis is inclined at an angle θ to the plate, the moment of inertia is given by:
I = I0 + m * L^2 * sin^2(θ)
- Where I0 is the moment of inertia about an axis perpendicular to the plate and passing through its center of mass.
4. Substitute Values:
- Substituting the given values into the formula:
I = (m * L^2) / 3 + m * L^2 * sin^2(15°)
5. Numerical Calculation:
- Calculate the moment of inertia using the above formula and the numerical values of mass, edge length, and angle.
6. Importance of Moment of Inertia:
- Moment of inertia is a crucial concept in rotational dynamics as it determines the resistance of an object to changes in its rotational motion.
By following the steps mentioned above, you can calculate the moment of inertia of a square plate about an axis in its plane passing through one of its vertices at an angle of 15° with its side.
1. Given Parameters:
- Mass of the plate, m
- Edge length of the square plate, L
- Angle between the axis and the plate's side, 15°
2. Moment of Inertia Formula:
- Moment of inertia (I) of a plate about an axis in its plane passing through one of its vertices can be calculated using the formula:
I = (m * L^2) / 3
3. Calculation with Angle:
- When the axis is inclined at an angle θ to the plate, the moment of inertia is given by:
I = I0 + m * L^2 * sin^2(θ)
- Where I0 is the moment of inertia about an axis perpendicular to the plate and passing through its center of mass.
4. Substitute Values:
- Substituting the given values into the formula:
I = (m * L^2) / 3 + m * L^2 * sin^2(15°)
5. Numerical Calculation:
- Calculate the moment of inertia using the above formula and the numerical values of mass, edge length, and angle.
6. Importance of Moment of Inertia:
- Moment of inertia is a crucial concept in rotational dynamics as it determines the resistance of an object to changes in its rotational motion.
By following the steps mentioned above, you can calculate the moment of inertia of a square plate about an axis in its plane passing through one of its vertices at an angle of 15° with its side.
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A square plate of mass m and edge L is shown in the figure moment of intertia of the plate about the axis in the plane of plate and passing through one of its vertex making an angle 15° with its side Related: Rotational Motion and Moment of Inertia - System of Particles and Rotational Motion, Class 11, Physi
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A square plate of mass m and edge L is shown in the figure moment of intertia of the plate about the axis in the plane of plate and passing through one of its vertex making an angle 15° with its side Related: Rotational Motion and Moment of Inertia - System of Particles and Rotational Motion, Class 11, Physi for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A square plate of mass m and edge L is shown in the figure moment of intertia of the plate about the axis in the plane of plate and passing through one of its vertex making an angle 15° with its side Related: Rotational Motion and Moment of Inertia - System of Particles and Rotational Motion, Class 11, Physi covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A square plate of mass m and edge L is shown in the figure moment of intertia of the plate about the axis in the plane of plate and passing through one of its vertex making an angle 15° with its side Related: Rotational Motion and Moment of Inertia - System of Particles and Rotational Motion, Class 11, Physi.
A square plate of mass m and edge L is shown in the figure moment of intertia of the plate about the axis in the plane of plate and passing through one of its vertex making an angle 15° with its side Related: Rotational Motion and Moment of Inertia - System of Particles and Rotational Motion, Class 11, Physi for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A square plate of mass m and edge L is shown in the figure moment of intertia of the plate about the axis in the plane of plate and passing through one of its vertex making an angle 15° with its side Related: Rotational Motion and Moment of Inertia - System of Particles and Rotational Motion, Class 11, Physi covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A square plate of mass m and edge L is shown in the figure moment of intertia of the plate about the axis in the plane of plate and passing through one of its vertex making an angle 15° with its side Related: Rotational Motion and Moment of Inertia - System of Particles and Rotational Motion, Class 11, Physi.
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