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A rotating solid cylinder of mass M and radius R is brought to rest on a flat surface with coefficient of kinetic friction myu . Evaluate the magnitude of its angular deceleration if it has pure rotation about its central axis?
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Introduction:
When a rotating solid cylinder is brought to rest on a flat surface with a coefficient of kinetic friction, it experiences a deceleration in its angular velocity. In this explanation, we will calculate the magnitude of this angular deceleration.
Given:
- Mass of the cylinder (M)
- Radius of the cylinder (R)
- Coefficient of kinetic friction (μ)
Approach:
To find the angular deceleration, we can use the relation between torque and angular acceleration. The torque acting on the cylinder is due to the frictional force acting on it.
Step 1: Determine the frictional force:
The frictional force acting on the cylinder can be calculated using the equation:
Ffriction = μ * Normal force
The normal force is equal to the weight of the cylinder, which is given by:
Normal force = M * g
Where g is the acceleration due to gravity. Therefore, the frictional force can be written as:
Ffriction = μ * M * g
Step 2: Calculate the torque:
The torque acting on the cylinder is given by the product of the frictional force and the radius of the cylinder:
Torque = Ffriction * R
Step 3: Find the angular deceleration:
The angular deceleration (α) can be calculated using the equation:
Torque = Moment of inertia * Angular acceleration
The moment of inertia (I) for a solid cylinder rotating about its central axis is given by:
Moment of inertia (I) = (1/2) * M * R^2
Substituting the values into the equation, we get:
Torque = (1/2) * M * R^2 * α
Now, equating the two equations for torque, we can solve for α:
(1/2) * M * R^2 * α = Ffriction * R
α = (2 * Ffriction) / (M * R)
Conclusion:
The magnitude of the angular deceleration of the rotating solid cylinder can be calculated using the equation α = (2 * Ffriction) / (M * R), where Ffriction is the frictional force given by Ffriction = μ * M * g.
When a rotating solid cylinder is brought to rest on a flat surface with a coefficient of kinetic friction, it experiences a deceleration in its angular velocity. In this explanation, we will calculate the magnitude of this angular deceleration.
Given:
- Mass of the cylinder (M)
- Radius of the cylinder (R)
- Coefficient of kinetic friction (μ)
Approach:
To find the angular deceleration, we can use the relation between torque and angular acceleration. The torque acting on the cylinder is due to the frictional force acting on it.
Step 1: Determine the frictional force:
The frictional force acting on the cylinder can be calculated using the equation:
Ffriction = μ * Normal force
The normal force is equal to the weight of the cylinder, which is given by:
Normal force = M * g
Where g is the acceleration due to gravity. Therefore, the frictional force can be written as:
Ffriction = μ * M * g
Step 2: Calculate the torque:
The torque acting on the cylinder is given by the product of the frictional force and the radius of the cylinder:
Torque = Ffriction * R
Step 3: Find the angular deceleration:
The angular deceleration (α) can be calculated using the equation:
Torque = Moment of inertia * Angular acceleration
The moment of inertia (I) for a solid cylinder rotating about its central axis is given by:
Moment of inertia (I) = (1/2) * M * R^2
Substituting the values into the equation, we get:
Torque = (1/2) * M * R^2 * α
Now, equating the two equations for torque, we can solve for α:
(1/2) * M * R^2 * α = Ffriction * R
α = (2 * Ffriction) / (M * R)
Conclusion:
The magnitude of the angular deceleration of the rotating solid cylinder can be calculated using the equation α = (2 * Ffriction) / (M * R), where Ffriction is the frictional force given by Ffriction = μ * M * g.
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A rotating solid cylinder of mass M and radius R is brought to rest on a flat surface with coefficient of kinetic friction myu . Evaluate the magnitude of its angular deceleration if it has pure rotation about its central axis?
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A rotating solid cylinder of mass M and radius R is brought to rest on a flat surface with coefficient of kinetic friction myu . Evaluate the magnitude of its angular deceleration if it has pure rotation about its central axis? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A rotating solid cylinder of mass M and radius R is brought to rest on a flat surface with coefficient of kinetic friction myu . Evaluate the magnitude of its angular deceleration if it has pure rotation about its central axis? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A rotating solid cylinder of mass M and radius R is brought to rest on a flat surface with coefficient of kinetic friction myu . Evaluate the magnitude of its angular deceleration if it has pure rotation about its central axis?.
A rotating solid cylinder of mass M and radius R is brought to rest on a flat surface with coefficient of kinetic friction myu . Evaluate the magnitude of its angular deceleration if it has pure rotation about its central axis? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A rotating solid cylinder of mass M and radius R is brought to rest on a flat surface with coefficient of kinetic friction myu . Evaluate the magnitude of its angular deceleration if it has pure rotation about its central axis? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A rotating solid cylinder of mass M and radius R is brought to rest on a flat surface with coefficient of kinetic friction myu . Evaluate the magnitude of its angular deceleration if it has pure rotation about its central axis?.
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