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Homogeneous disc of mass 2 kg and radius 15 cm is rotating about its axis (which is fixed) with an angular velocity of 4 radian/sec. The linear momentum of the disc is 1.2 kg m/sec 1.0 kg m/sec 0.6 kg m/sec None of the above?
Verified Answer
Homogeneous disc of mass 2 kg and radius 15 cm is rotating about its a...
The formula for angular momentum is:
L = Iw, where is the angular velocity and I is the moment of inertia.
For a disk,
I = 1/2*MR^2, where M is the mass of the disk and R is the radius of the disk.
For this disk,
I = 1/2*MR^2 = 1/2*(2) x (0.15)^2 = 0.0225kgm^2
L = Iw = 0.0225kgm^2 x (4rad/s) = 0.09kgm^2 rad/s
The linear momentum is related to the angular momentum by the formula; L = pr.
We can solve for p, the linear momentum in this equation to get,
p = L/r = 0.09/0.15 = 0.6kgs
L = Iw, where is the angular velocity and I is the moment of inertia.
For a disk,
I = 1/2*MR^2, where M is the mass of the disk and R is the radius of the disk.
For this disk,
I = 1/2*MR^2 = 1/2*(2) x (0.15)^2 = 0.0225kgm^2
L = Iw = 0.0225kgm^2 x (4rad/s) = 0.09kgm^2 rad/s
The linear momentum is related to the angular momentum by the formula; L = pr.
We can solve for p, the linear momentum in this equation to get,
p = L/r = 0.09/0.15 = 0.6kgs
This question is part of UPSC exam. View all NEET courses
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Homogeneous disc of mass 2 kg and radius 15 cm is rotating about its a...
Angular Velocity and Linear Velocity Relationship
Angular velocity (ω) is the rate of change of angular displacement with respect to time. Linear velocity (v) is the rate of change of linear displacement with respect to time. There is a relationship between angular velocity and linear velocity.
The equation that relates angular velocity and linear velocity is given by:
v = ω * r
Where:
v = linear velocity
ω = angular velocity
r = radius of rotation
Given data:
Mass of the disc (m) = 2 kg
Radius of the disc (r) = 15 cm = 0.15 m
Angular velocity of the disc (ω) = 4 rad/s
Calculating Linear Velocity
Using the equation v = ω * r, we can calculate the linear velocity of the disc.
v = 4 rad/s * 0.15 m
v = 0.6 m/s
Therefore, the linear velocity of the disc is 0.6 m/s.
Calculating Linear Momentum
Linear momentum (p) is defined as the product of mass and linear velocity. The equation for linear momentum is given by:
p = m * v
Where:
p = linear momentum
m = mass
v = linear velocity
Substituting the given values, we can calculate the linear momentum of the disc.
p = 2 kg * 0.6 m/s
p = 1.2 kg m/s
Therefore, the linear momentum of the disc is 1.2 kg m/s.
Conclusion
The linear momentum of the disc is 1.2 kg m/s. Therefore, the correct answer is option A: 1.2 kg m/s.
Angular velocity (ω) is the rate of change of angular displacement with respect to time. Linear velocity (v) is the rate of change of linear displacement with respect to time. There is a relationship between angular velocity and linear velocity.
The equation that relates angular velocity and linear velocity is given by:
v = ω * r
Where:
v = linear velocity
ω = angular velocity
r = radius of rotation
Given data:
Mass of the disc (m) = 2 kg
Radius of the disc (r) = 15 cm = 0.15 m
Angular velocity of the disc (ω) = 4 rad/s
Calculating Linear Velocity
Using the equation v = ω * r, we can calculate the linear velocity of the disc.
v = 4 rad/s * 0.15 m
v = 0.6 m/s
Therefore, the linear velocity of the disc is 0.6 m/s.
Calculating Linear Momentum
Linear momentum (p) is defined as the product of mass and linear velocity. The equation for linear momentum is given by:
p = m * v
Where:
p = linear momentum
m = mass
v = linear velocity
Substituting the given values, we can calculate the linear momentum of the disc.
p = 2 kg * 0.6 m/s
p = 1.2 kg m/s
Therefore, the linear momentum of the disc is 1.2 kg m/s.
Conclusion
The linear momentum of the disc is 1.2 kg m/s. Therefore, the correct answer is option A: 1.2 kg m/s.
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Homogeneous disc of mass 2 kg and radius 15 cm is rotating about its axis (which is fixed) with an angular velocity of 4 radian/sec. The linear momentum of the disc is 1.2 kg m/sec 1.0 kg m/sec 0.6 kg m/sec None of the above?
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Homogeneous disc of mass 2 kg and radius 15 cm is rotating about its axis (which is fixed) with an angular velocity of 4 radian/sec. The linear momentum of the disc is 1.2 kg m/sec 1.0 kg m/sec 0.6 kg m/sec None of the above? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Homogeneous disc of mass 2 kg and radius 15 cm is rotating about its axis (which is fixed) with an angular velocity of 4 radian/sec. The linear momentum of the disc is 1.2 kg m/sec 1.0 kg m/sec 0.6 kg m/sec None of the above? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Homogeneous disc of mass 2 kg and radius 15 cm is rotating about its axis (which is fixed) with an angular velocity of 4 radian/sec. The linear momentum of the disc is 1.2 kg m/sec 1.0 kg m/sec 0.6 kg m/sec None of the above?.
Homogeneous disc of mass 2 kg and radius 15 cm is rotating about its axis (which is fixed) with an angular velocity of 4 radian/sec. The linear momentum of the disc is 1.2 kg m/sec 1.0 kg m/sec 0.6 kg m/sec None of the above? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Homogeneous disc of mass 2 kg and radius 15 cm is rotating about its axis (which is fixed) with an angular velocity of 4 radian/sec. The linear momentum of the disc is 1.2 kg m/sec 1.0 kg m/sec 0.6 kg m/sec None of the above? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Homogeneous disc of mass 2 kg and radius 15 cm is rotating about its axis (which is fixed) with an angular velocity of 4 radian/sec. The linear momentum of the disc is 1.2 kg m/sec 1.0 kg m/sec 0.6 kg m/sec None of the above?.
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