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A flywheel in the form of a solid circular disc of radius 100 mm and uniform thickness has a mass of 10 kg. If it is rotating at a uniform angular velocity of 20 rad/s, the kinetic energy (in J) of the flywheel is _______
Correct answer is '9.9 to 10.1'. Can you explain this answer?
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A flywheel in the form of a solid circular disc of radius 100 mm and u...
Given data:
- Radius of the flywheel (r) = 100 mm = 0.1 m
- Mass of the flywheel (m) = 10 kg
- Angular velocity of the flywheel (ω) = 20 rad/s

Formula:
The kinetic energy (KE) of a rotating object can be calculated using the formula:
KE = 1/2 * I * ω²

Where:
- KE is the kinetic energy
- I is the moment of inertia
- ω is the angular velocity

Calculating the moment of inertia (I):
The moment of inertia of a solid circular disc can be calculated using the formula:
I = (1/2) * m * r²

Substituting the given values:
I = (1/2) * 10 * (0.1)²
I = 0.05 kg.m²

Calculating the kinetic energy (KE):
Using the formula mentioned above:
KE = 1/2 * 0.05 * (20)²
KE = 0.05 * 400
KE = 20 J

Explanation:
The kinetic energy of the flywheel is calculated using the formula KE = 1/2 * I * ω², where I is the moment of inertia and ω is the angular velocity.

First, we calculate the moment of inertia using the formula I = (1/2) * m * r², where m is the mass of the flywheel and r is the radius. Substituting the given values, we find that the moment of inertia is 0.05 kg.m².

Then, we substitute the moment of inertia and the given angular velocity into the formula for kinetic energy. After simplifying the expression, we find that the kinetic energy of the flywheel is 20 J.

Therefore, the correct answer is between 9.9 to 10.1 J, as stated.
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A flywheel in the form of a solid circular disc of radius 100 mm and uniform thickness has a mass of 10 kg. If it is rotating at a uniform angular velocity of 20 rad/s, the kinetic energy (in J) of the flywheel is _______Correct answer is '9.9 to 10.1'. Can you explain this answer?
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A flywheel in the form of a solid circular disc of radius 100 mm and uniform thickness has a mass of 10 kg. If it is rotating at a uniform angular velocity of 20 rad/s, the kinetic energy (in J) of the flywheel is _______Correct answer is '9.9 to 10.1'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A flywheel in the form of a solid circular disc of radius 100 mm and uniform thickness has a mass of 10 kg. If it is rotating at a uniform angular velocity of 20 rad/s, the kinetic energy (in J) of the flywheel is _______Correct answer is '9.9 to 10.1'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A flywheel in the form of a solid circular disc of radius 100 mm and uniform thickness has a mass of 10 kg. If it is rotating at a uniform angular velocity of 20 rad/s, the kinetic energy (in J) of the flywheel is _______Correct answer is '9.9 to 10.1'. Can you explain this answer?.
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