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A hoop of mass M and radius R rolls without slipping along a straight line on a horizontal surface as shown in the figure. A point mass m slides without friction along the inner surface of the hoop, performing small oscillations about the mean position. The number of degrees of freedom of the system (in integer) is?
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A hoop of mass M and radius R rolls without slipping along a straight ...
The number of degrees of freedom of the system:
The system consists of a hoop of mass M and radius R rolling without slipping along a straight line on a horizontal surface, with a point mass m sliding without friction along the inner surface of the hoop and performing small oscillations about the mean position.
In order to determine the number of degrees of freedom of the system, we need to consider the independent variables that define the configuration of the system.
1. Translational motion of the hoop:
The hoop can move along the straight line on the horizontal surface, which can be described by a single independent variable, such as the position of the center of mass of the hoop along the line. This corresponds to 1 degree of freedom.
2. Rotational motion of the hoop:
The hoop can also rotate about its center as it rolls without slipping. Since the hoop is constrained to roll without slipping, the rotational motion is not independent of the translational motion. In this case, the rotational motion can be described by the angle of rotation of the hoop, which is related to the translational motion by the equation θ = s/R, where θ is the angle of rotation and s is the displacement of the center of mass of the hoop along the line. Therefore, the rotational motion adds 0 degrees of freedom to the system.
3. Oscillatory motion of the point mass:
The point mass m slides without friction along the inner surface of the hoop and performs small oscillations about the mean position. The oscillatory motion can be described by the displacement of the point mass from the mean position, which corresponds to 1 degree of freedom.
Therefore, the total number of degrees of freedom of the system is 1 + 0 + 1 = 2.
Conclusion:
The system consisting of a hoop of mass M and radius R rolling without slipping along a straight line on a horizontal surface, with a point mass m sliding without friction along the inner surface of the hoop and performing small oscillations about the mean position, has 2 degrees of freedom.
The system consists of a hoop of mass M and radius R rolling without slipping along a straight line on a horizontal surface, with a point mass m sliding without friction along the inner surface of the hoop and performing small oscillations about the mean position.
In order to determine the number of degrees of freedom of the system, we need to consider the independent variables that define the configuration of the system.
1. Translational motion of the hoop:
The hoop can move along the straight line on the horizontal surface, which can be described by a single independent variable, such as the position of the center of mass of the hoop along the line. This corresponds to 1 degree of freedom.
2. Rotational motion of the hoop:
The hoop can also rotate about its center as it rolls without slipping. Since the hoop is constrained to roll without slipping, the rotational motion is not independent of the translational motion. In this case, the rotational motion can be described by the angle of rotation of the hoop, which is related to the translational motion by the equation θ = s/R, where θ is the angle of rotation and s is the displacement of the center of mass of the hoop along the line. Therefore, the rotational motion adds 0 degrees of freedom to the system.
3. Oscillatory motion of the point mass:
The point mass m slides without friction along the inner surface of the hoop and performs small oscillations about the mean position. The oscillatory motion can be described by the displacement of the point mass from the mean position, which corresponds to 1 degree of freedom.
Therefore, the total number of degrees of freedom of the system is 1 + 0 + 1 = 2.
Conclusion:
The system consisting of a hoop of mass M and radius R rolling without slipping along a straight line on a horizontal surface, with a point mass m sliding without friction along the inner surface of the hoop and performing small oscillations about the mean position, has 2 degrees of freedom.
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A hoop of mass M and radius R rolls without slipping along a straight line on a horizontal surface as shown in the figure. A point mass m slides without friction along the inner surface of the hoop, performing small oscillations about the mean position. The number of degrees of freedom of the system (in integer) is?
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A hoop of mass M and radius R rolls without slipping along a straight line on a horizontal surface as shown in the figure. A point mass m slides without friction along the inner surface of the hoop, performing small oscillations about the mean position. The number of degrees of freedom of the system (in integer) is? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about A hoop of mass M and radius R rolls without slipping along a straight line on a horizontal surface as shown in the figure. A point mass m slides without friction along the inner surface of the hoop, performing small oscillations about the mean position. The number of degrees of freedom of the system (in integer) is? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A hoop of mass M and radius R rolls without slipping along a straight line on a horizontal surface as shown in the figure. A point mass m slides without friction along the inner surface of the hoop, performing small oscillations about the mean position. The number of degrees of freedom of the system (in integer) is?.
A hoop of mass M and radius R rolls without slipping along a straight line on a horizontal surface as shown in the figure. A point mass m slides without friction along the inner surface of the hoop, performing small oscillations about the mean position. The number of degrees of freedom of the system (in integer) is? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about A hoop of mass M and radius R rolls without slipping along a straight line on a horizontal surface as shown in the figure. A point mass m slides without friction along the inner surface of the hoop, performing small oscillations about the mean position. The number of degrees of freedom of the system (in integer) is? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A hoop of mass M and radius R rolls without slipping along a straight line on a horizontal surface as shown in the figure. A point mass m slides without friction along the inner surface of the hoop, performing small oscillations about the mean position. The number of degrees of freedom of the system (in integer) is?.
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A hoop of mass M and radius R rolls without slipping along a straight line on a horizontal surface as shown in the figure. A point mass m slides without friction along the inner surface of the hoop, performing small oscillations about the mean position. The number of degrees of freedom of the system (in integer) is?, a detailed solution for A hoop of mass M and radius R rolls without slipping along a straight line on a horizontal surface as shown in the figure. A point mass m slides without friction along the inner surface of the hoop, performing small oscillations about the mean position. The number of degrees of freedom of the system (in integer) is? has been provided alongside types of A hoop of mass M and radius R rolls without slipping along a straight line on a horizontal surface as shown in the figure. A point mass m slides without friction along the inner surface of the hoop, performing small oscillations about the mean position. The number of degrees of freedom of the system (in integer) is? theory, EduRev gives you an
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