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A uniform circular disc of mass m and radius r is having a point mass m at its circumference is performing rolling without sleeping over the horizontal surface as shown acceleration of point o is a not towards tight if and is a normal reaction on disc by the horizontal surface at this instant then?
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A uniform circular disc of mass m and radius r is having a point mass ...
Understanding the System
In this scenario, we have a uniform circular disc of mass m and radius r, with a point mass m attached at its circumference. The disc is rolling without slipping on a horizontal surface. The key points to consider involve the forces acting on the disc and the acceleration of the point O, which is the center of the disc.
Forces Acting on the Disc
- The weight of the disc and the point mass acts downwards:
- Total weight = m (for disc) + m (for point mass) = 2m
- The normal reaction (N) from the surface acts upwards on the disc.
- The disc also experiences frictional force (f) that prevents slipping.
Acceleration of Point O
- Point O (center of the disc) has a linear acceleration a towards the right.
- The point mass at the circumference has both translational and rotational motion, contributing to its acceleration.
Equations of Motion
- For rolling without slipping, the relationship between linear acceleration (a) and angular acceleration (α) is given by:
a = rα
- The net force acting on the system is given by:
N - 2mg = 0, leading to N = 2mg.
Normal Reaction at this Instant
- The normal reaction N acting on the disc by the horizontal surface is equal to the total weight of the disc and point mass, thus:
N = 2mg.
- This indicates that the disc supports its own weight and the weight of the point mass, maintaining equilibrium in the vertical direction.
Conclusion
In summary, the normal reaction on the disc at this instant is:
N = 2mg.
This analysis reveals how forces are balanced in a rolling system and emphasizes the importance of understanding the dynamics involved.
In this scenario, we have a uniform circular disc of mass m and radius r, with a point mass m attached at its circumference. The disc is rolling without slipping on a horizontal surface. The key points to consider involve the forces acting on the disc and the acceleration of the point O, which is the center of the disc.
Forces Acting on the Disc
- The weight of the disc and the point mass acts downwards:
- Total weight = m (for disc) + m (for point mass) = 2m
- The normal reaction (N) from the surface acts upwards on the disc.
- The disc also experiences frictional force (f) that prevents slipping.
Acceleration of Point O
- Point O (center of the disc) has a linear acceleration a towards the right.
- The point mass at the circumference has both translational and rotational motion, contributing to its acceleration.
Equations of Motion
- For rolling without slipping, the relationship between linear acceleration (a) and angular acceleration (α) is given by:
a = rα
- The net force acting on the system is given by:
N - 2mg = 0, leading to N = 2mg.
Normal Reaction at this Instant
- The normal reaction N acting on the disc by the horizontal surface is equal to the total weight of the disc and point mass, thus:
N = 2mg.
- This indicates that the disc supports its own weight and the weight of the point mass, maintaining equilibrium in the vertical direction.
Conclusion
In summary, the normal reaction on the disc at this instant is:
N = 2mg.
This analysis reveals how forces are balanced in a rolling system and emphasizes the importance of understanding the dynamics involved.
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A uniform circular disc of mass m and radius r is having a point mass m at its circumference is performing rolling without sleeping over the horizontal surface as shown acceleration of point o is a not towards tight if and is a normal reaction on disc by the horizontal surface at this instant then?
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A uniform circular disc of mass m and radius r is having a point mass m at its circumference is performing rolling without sleeping over the horizontal surface as shown acceleration of point o is a not towards tight if and is a normal reaction on disc by the horizontal surface at this instant then? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A uniform circular disc of mass m and radius r is having a point mass m at its circumference is performing rolling without sleeping over the horizontal surface as shown acceleration of point o is a not towards tight if and is a normal reaction on disc by the horizontal surface at this instant then? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A uniform circular disc of mass m and radius r is having a point mass m at its circumference is performing rolling without sleeping over the horizontal surface as shown acceleration of point o is a not towards tight if and is a normal reaction on disc by the horizontal surface at this instant then?.
A uniform circular disc of mass m and radius r is having a point mass m at its circumference is performing rolling without sleeping over the horizontal surface as shown acceleration of point o is a not towards tight if and is a normal reaction on disc by the horizontal surface at this instant then? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A uniform circular disc of mass m and radius r is having a point mass m at its circumference is performing rolling without sleeping over the horizontal surface as shown acceleration of point o is a not towards tight if and is a normal reaction on disc by the horizontal surface at this instant then? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A uniform circular disc of mass m and radius r is having a point mass m at its circumference is performing rolling without sleeping over the horizontal surface as shown acceleration of point o is a not towards tight if and is a normal reaction on disc by the horizontal surface at this instant then?.
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