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If a gymnast, sitting on a rotating stool with his arms outstretched, suddenly lowers his hands
- a)The angular velocity decreases
- b)His moment of inertia decreases
- c)The angular velocity stays constant
- d)The angular momentum increases
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
If a gymnast, sitting on a rotating stool with his arms outstretched, ...
Explanation:
When a gymnast sitting on a rotating stool lowers his hands, the moment of inertia decreases.
Moment of Inertia:
Moment of inertia is a measure of an object's resistance to changes in its rotational motion. It depends on the mass distribution of the object and the axis of rotation. In simple terms, it is a property of an object that determines how difficult it is to change its rotation.
Effect of Lowering Hands:
Lowering the hands of the gymnast changes the distribution of mass in the system. This change in mass distribution affects the moment of inertia.
Decrease in Moment of Inertia:
When the gymnast lowers his hands, the mass that was previously farther away from the axis of rotation (arms outstretched) is brought closer to the axis of rotation. This reduces the moment of inertia.
Explanation in Terms of Equation:
The moment of inertia (I) depends on the mass (m) and the distance (r) of the mass from the axis of rotation. It can be mathematically represented as:
I = m * r^2
When the gymnast lowers his hands, the distance (r) decreases, resulting in a decrease in the moment of inertia (I).
Effect on Angular Velocity:
Angular velocity (ω) is the rate at which an object rotates around an axis. It is given by the equation:
ω = v / r
where v is the linear velocity and r is the distance from the axis of rotation.
Since the mass distribution of the gymnast changes, the linear velocity (v) of the gymnast's hands also changes. However, the distance (r) decreases, which compensates for the change in linear velocity, thus keeping the angular velocity constant.
Therefore, the correct answer is option 'B': His moment of inertia decreases.
When a gymnast sitting on a rotating stool lowers his hands, the moment of inertia decreases.
Moment of Inertia:
Moment of inertia is a measure of an object's resistance to changes in its rotational motion. It depends on the mass distribution of the object and the axis of rotation. In simple terms, it is a property of an object that determines how difficult it is to change its rotation.
Effect of Lowering Hands:
Lowering the hands of the gymnast changes the distribution of mass in the system. This change in mass distribution affects the moment of inertia.
Decrease in Moment of Inertia:
When the gymnast lowers his hands, the mass that was previously farther away from the axis of rotation (arms outstretched) is brought closer to the axis of rotation. This reduces the moment of inertia.
Explanation in Terms of Equation:
The moment of inertia (I) depends on the mass (m) and the distance (r) of the mass from the axis of rotation. It can be mathematically represented as:
I = m * r^2
When the gymnast lowers his hands, the distance (r) decreases, resulting in a decrease in the moment of inertia (I).
Effect on Angular Velocity:
Angular velocity (ω) is the rate at which an object rotates around an axis. It is given by the equation:
ω = v / r
where v is the linear velocity and r is the distance from the axis of rotation.
Since the mass distribution of the gymnast changes, the linear velocity (v) of the gymnast's hands also changes. However, the distance (r) decreases, which compensates for the change in linear velocity, thus keeping the angular velocity constant.
Therefore, the correct answer is option 'B': His moment of inertia decreases.
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Community Answer
If a gymnast, sitting on a rotating stool with his arms outstretched, ...
MI=MR2^
hence when R decreases MI decreases
hence when R decreases MI decreases
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If a gymnast, sitting on a rotating stool with his arms outstretched, suddenly lowers his handsa)The angular velocity decreasesb)His moment of inertia decreasesc)The angular velocity stays constantd)The angular momentum increasesCorrect answer is option 'B'. Can you explain this answer?
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If a gymnast, sitting on a rotating stool with his arms outstretched, suddenly lowers his handsa)The angular velocity decreasesb)His moment of inertia decreasesc)The angular velocity stays constantd)The angular momentum increasesCorrect answer is option 'B'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about If a gymnast, sitting on a rotating stool with his arms outstretched, suddenly lowers his handsa)The angular velocity decreasesb)His moment of inertia decreasesc)The angular velocity stays constantd)The angular momentum increasesCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a gymnast, sitting on a rotating stool with his arms outstretched, suddenly lowers his handsa)The angular velocity decreasesb)His moment of inertia decreasesc)The angular velocity stays constantd)The angular momentum increasesCorrect answer is option 'B'. Can you explain this answer?.
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