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A stepped disc of mass m inner and outer radius r and R respectively is placed on a smooth horizontal surface. It is wrapped by a thread which is pulled by a horizontal force F. If the radius of gyration of the disc is k, find:
(i) the acceleration of CM of the disc
(ii) the angular acceleration of the disc.?
(i) the acceleration of CM of the disc
(ii) the angular acceleration of the disc.?
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A stepped disc of mass m inner and outer radius r and R respectively i...
Acceleration of CM of the disc:
Acceleration of CM of the disc can be calculated using Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration.
• The net force acting on the disc is the horizontal component of the force F, which is F.
• The mass of the disc is m.
• The acceleration of the CM of the disc is denoted by a.
Using Newton's second law,
F = ma
a = F/m
Therefore, the acceleration of the CM of the disc is given by a = F/m.
Angular acceleration of the disc:
Angular acceleration of the disc can be calculated using the torque equation, which states that the net torque acting on an object is equal to the product of its moment of inertia and angular acceleration.
• The net torque acting on the disc is the torque due to the force F, which is F multiplied by the radius of gyration k.
• The moment of inertia of the disc is denoted by I.
• The angular acceleration of the disc is denoted by α.
The torque equation can be written as
τ = Iα
Fk = Iα
α = Fk/I
Since the disc is a stepped disc, the moment of inertia I can be calculated using the parallel axis theorem for a disc with inner and outer radii.
Therefore, the angular acceleration of the disc is given by α = Fk/I.
Acceleration of CM of the disc can be calculated using Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration.
• The net force acting on the disc is the horizontal component of the force F, which is F.
• The mass of the disc is m.
• The acceleration of the CM of the disc is denoted by a.
Using Newton's second law,
F = ma
a = F/m
Therefore, the acceleration of the CM of the disc is given by a = F/m.
Angular acceleration of the disc:
Angular acceleration of the disc can be calculated using the torque equation, which states that the net torque acting on an object is equal to the product of its moment of inertia and angular acceleration.
• The net torque acting on the disc is the torque due to the force F, which is F multiplied by the radius of gyration k.
• The moment of inertia of the disc is denoted by I.
• The angular acceleration of the disc is denoted by α.
The torque equation can be written as
τ = Iα
Fk = Iα
α = Fk/I
Since the disc is a stepped disc, the moment of inertia I can be calculated using the parallel axis theorem for a disc with inner and outer radii.
Therefore, the angular acceleration of the disc is given by α = Fk/I.
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A stepped disc of mass m inner and outer radius r and R respectively is placed on a smooth horizontal surface. It is wrapped by a thread which is pulled by a horizontal force F. If the radius of gyration of the disc is k, find:(i) the acceleration of CM of the disc (ii) the angular acceleration of the disc.?
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A stepped disc of mass m inner and outer radius r and R respectively is placed on a smooth horizontal surface. It is wrapped by a thread which is pulled by a horizontal force F. If the radius of gyration of the disc is k, find:(i) the acceleration of CM of the disc (ii) the angular acceleration of the disc.? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A stepped disc of mass m inner and outer radius r and R respectively is placed on a smooth horizontal surface. It is wrapped by a thread which is pulled by a horizontal force F. If the radius of gyration of the disc is k, find:(i) the acceleration of CM of the disc (ii) the angular acceleration of the disc.? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A stepped disc of mass m inner and outer radius r and R respectively is placed on a smooth horizontal surface. It is wrapped by a thread which is pulled by a horizontal force F. If the radius of gyration of the disc is k, find:(i) the acceleration of CM of the disc (ii) the angular acceleration of the disc.?.
A stepped disc of mass m inner and outer radius r and R respectively is placed on a smooth horizontal surface. It is wrapped by a thread which is pulled by a horizontal force F. If the radius of gyration of the disc is k, find:(i) the acceleration of CM of the disc (ii) the angular acceleration of the disc.? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A stepped disc of mass m inner and outer radius r and R respectively is placed on a smooth horizontal surface. It is wrapped by a thread which is pulled by a horizontal force F. If the radius of gyration of the disc is k, find:(i) the acceleration of CM of the disc (ii) the angular acceleration of the disc.? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A stepped disc of mass m inner and outer radius r and R respectively is placed on a smooth horizontal surface. It is wrapped by a thread which is pulled by a horizontal force F. If the radius of gyration of the disc is k, find:(i) the acceleration of CM of the disc (ii) the angular acceleration of the disc.?.
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A stepped disc of mass m inner and outer radius r and R respectively is placed on a smooth horizontal surface. It is wrapped by a thread which is pulled by a horizontal force F. If the radius of gyration of the disc is k, find:(i) the acceleration of CM of the disc (ii) the angular acceleration of the disc.?, a detailed solution for A stepped disc of mass m inner and outer radius r and R respectively is placed on a smooth horizontal surface. It is wrapped by a thread which is pulled by a horizontal force F. If the radius of gyration of the disc is k, find:(i) the acceleration of CM of the disc (ii) the angular acceleration of the disc.? has been provided alongside types of A stepped disc of mass m inner and outer radius r and R respectively is placed on a smooth horizontal surface. It is wrapped by a thread which is pulled by a horizontal force F. If the radius of gyration of the disc is k, find:(i) the acceleration of CM of the disc (ii) the angular acceleration of the disc.? theory, EduRev gives you an
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