
(a)
The axis of spin in the second and final parts of the gymnast’s routine.
Introduction:
Center of mass is that virtual point of the body where its complete mass is assumed to be concentrated.
Explanation:
The center of mass of an average human body lies near about its navel.
Gymnast spins about the center of mass of her body (near about navel of her) in the second and final parts of her routine. In the second part, she rotates in the tuck posture (position at B). In the final part, she straightens out (position at C).
Conclusion:
Thus, gymnast spins about the center of mass of her body in the second and final parts of her routine.
(b)
To Rank: The moment of inertia in three given positions from the greatest to the least.
The order of moment of inertia is,
Introduction:
The moment of inertia is defined as the property of body which resist the angular motion of the body. It is directly proportional to the product of mass and square of distance from the axis of rotation.
Where,
Explanation:
The initial position of the gymnast was at point
In overall process, her mass did not change but distance of center of mass (
If mass of object does not change then moment of inertia is directly proportional to the square of the distance from axis of rotation.
Therefore, the order of moment of inertia in decreasing order is:
Conclusion:
The moment of inertia was maximum at position
(c)
The order of angular velocity in three given positions from the greatest to the least.
Introduction:
The moment of inertia is defined as the property of body which resist the angular motion of the body. It is directly proportional to the product of mass and square of distance from the axis of rotation.
Where,
The angular momentum for a rigid body rotating about an axis is defined as the product of moment of inertia and angular velocity (
Where,
According to conservation of momentum when no external torque acting on the system then the angular momentum of the rigid body will conserve.
Therefore,
Explanation:
The initial position of the gymnast was at point
In overall process her mass did not change but distance of center of mass (
If mass of object does not change, then moment of inertia is directly proportional to the square of the distance from axis of rotation.
Therefore, the order of moment of inertia in decreasing order is:
And according to conservation of momentum,
When moment of inertia decreases, the angular velocity of rigid body should increase to make the product constant.
Thus, the order of angular velocity of gymnast at different points in decreasing order is:
Conclusion:
The angular velocity is maximum at point
(a)

Answer to Problem 89A
The order of moment of inertia is,
Explanation of Solution
Introduction:
Center of mass is that virtual point of the body where its complete mass is assumed to be concentrated.
The center of mass of an average human body lies near about its navel.
Gymnast spins about the center of mass of her body (near about navel of her) in the second and final parts of her routine. In the second part, she rotates in the tuck posture (position at B). In the final part, she straightens out (position at C).
Conclusion:
Thus, gymnast spins about the center of mass of her body in the second and final parts of her routine.
(b)
To Rank: The moment of inertia in three given positions from the greatest to the least.
(b)

Answer to Problem 89A
The order of moment of inertia is,
Explanation of Solution
Introduction:
The moment of inertia is defined as the property of body which resist the angular motion of the body. It is directly proportional to the product of mass and square of distance from the axis of rotation.
Where,
The initial position of the gymnast was at point
In overall process, her mass did not change but distance of center of mass (
If mass of object does not change then moment of inertia is directly proportional to the square of the distance from axis of rotation.
Therefore, the order of moment of inertia in decreasing order is:
Conclusion:
The moment of inertia was maximum at position
(c)
The order of
(c)

Answer to Problem 89A
Explanation of Solution
Introduction:
The moment of inertia is defined as the property of body which resist the angular motion of the body. It is directly proportional to the product of mass and square of distance from the axis of rotation.
Where,
The
Where,
According to conservation of momentum when no external torque acting on the system then the angular momentum of the rigid body will conserve.
Therefore,
The initial position of the gymnast was at point
In overall process her mass did not change but distance of center of mass (
If mass of object does not change, then moment of inertia is directly proportional to the square of the distance from axis of rotation.
Therefore, the order of moment of inertia in decreasing order is:
And according to conservation of momentum,
When moment of inertia decreases, the angular velocity of rigid body should increase to make the product constant.
Thus, the order of angular velocity of gymnast at different points in decreasing order is:
Conclusion:
The angular velocity is maximum at point
Chapter 9 Solutions
Glencoe Physics: Principles and Problems, Student Edition
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