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A block of mass m is kept on horizontal turntable at x distance from the centre. if coefficient of friction between block and surface of turntable is u, then maximum angular speed of the table so that block does not slip?
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A block of mass m is kept on horizontal turntable at x distance from t...
Maximum Angular Speed of Turntable
Introduction
When a block is kept on a horizontal turntable, and if the coefficient of friction between the block and the surface of turntable is known, then we can find out the maximum angular speed of the turntable so that the block does not slip. This is an important concept in physics.
Formula
The formula to calculate the maximum angular speed of the turntable is given by:
ω_max = u*g/x
- ω_max: Maximum angular speed of turntable (in radians per second)
- u: Coefficient of friction between block and surface of turntable
- g: Acceleration due to gravity (9.8 m/s²)
- x: Distance of block from the centre of turntable
Explanation
When the turntable starts to rotate, a centrifugal force acts on the block which tries to make it slip. This force can be calculated using the formula:
F_c = m*ω²*r
- F_c: Centrifugal force (in Newtons)
- m: Mass of the block (in kilograms)
- ω: Angular speed of turntable (in radians per second)
- r: Distance of block from the centre of turntable (in meters)
The maximum angular speed of turntable is the one where the centrifugal force is equal to the maximum frictional force that can be exerted on the block. This frictional force can be calculated using the formula:
F_f = u*m*g
- F_f: Maximum frictional force (in Newtons)
- u: Coefficient of friction between block and surface of turntable
- m: Mass of the block (in kilograms)
- g: Acceleration due to gravity (9.8 m/s²)
Equating the centrifugal force and maximum frictional force, we get:
m*ω²*r = u*m*g
Simplifying the equation, we get:
ω_max = u*g/r
As the distance of the block from the centre of turntable is x, we can substitute r with x to get:
ω_max = u*g/x
Conclusion
The maximum angular speed of the turntable can be calculated using the formula ω_max = u*g/x. This concept is important in physics and helps in understanding the behaviour
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A block of mass m is kept on horizontal turntable at x distance from t...
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A block of mass m is kept on horizontal turntable at x distance from the centre. if coefficient of friction between block and surface of turntable is u, then maximum angular speed of the table so that block does not slip?
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A block of mass m is kept on horizontal turntable at x distance from the centre. if coefficient of friction between block and surface of turntable is u, then maximum angular speed of the table so that block does not slip? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A block of mass m is kept on horizontal turntable at x distance from the centre. if coefficient of friction between block and surface of turntable is u, then maximum angular speed of the table so that block does not slip? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A block of mass m is kept on horizontal turntable at x distance from the centre. if coefficient of friction between block and surface of turntable is u, then maximum angular speed of the table so that block does not slip?.
A block of mass m is kept on horizontal turntable at x distance from the centre. if coefficient of friction between block and surface of turntable is u, then maximum angular speed of the table so that block does not slip? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A block of mass m is kept on horizontal turntable at x distance from the centre. if coefficient of friction between block and surface of turntable is u, then maximum angular speed of the table so that block does not slip? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A block of mass m is kept on horizontal turntable at x distance from the centre. if coefficient of friction between block and surface of turntable is u, then maximum angular speed of the table so that block does not slip?.
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