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A circular ring of diameter 40cm and mass 1kg is rotating about an axis normal to its plane and passing through the centre with a frequency of 10 rotations per second. Calculate the angular momentum about its axis of rotation?
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A circular ring of diameter 40cm and mass 1kg is rotating about an axi...
Given:
Diameter of the circular ring (d) = 40 cm
Radius of the circular ring (r) = d/2 = 20 cm = 0.2 m
Mass of the circular ring (m) = 1 kg
Frequency of rotation (f) = 10 rotations per second
Formula:
The formula to calculate angular momentum (L) is given by:
L = Iω
where,
I = Moment of inertia
ω = Angular velocity
Calculation:
Step 1: Convert the diameter of the circular ring from cm to m
Diameter (d) = 40 cm = 0.4 m
Step 2: Calculate the moment of inertia (I) of the circular ring
The moment of inertia of a circular ring rotating about an axis passing through its center and perpendicular to its plane is given by the formula:
I = 0.5 * m * r^2
where,
m = mass of the circular ring
r = radius of the circular ring
Substituting the values, we get:
I = 0.5 * 1 kg * (0.2 m)^2
I = 0.02 kg.m^2
Step 3: Calculate the angular velocity (ω) of the circular ring
Angular velocity (ω) is given by the formula:
ω = 2πf
where,
f = frequency of rotation
Substituting the values, we get:
ω = 2 * 3.14 * 10 rad/s
ω = 62.8 rad/s
Step 4: Calculate the angular momentum (L) of the circular ring
Using the formula L = Iω, we can calculate the angular momentum:
L = 0.02 kg.m^2 * 62.8 rad/s
L = 1.256 kg.m^2/s
Answer:
The angular momentum of the circular ring about its axis of rotation is 1.256 kg.m^2/s.
Diameter of the circular ring (d) = 40 cm
Radius of the circular ring (r) = d/2 = 20 cm = 0.2 m
Mass of the circular ring (m) = 1 kg
Frequency of rotation (f) = 10 rotations per second
Formula:
The formula to calculate angular momentum (L) is given by:
L = Iω
where,
I = Moment of inertia
ω = Angular velocity
Calculation:
Step 1: Convert the diameter of the circular ring from cm to m
Diameter (d) = 40 cm = 0.4 m
Step 2: Calculate the moment of inertia (I) of the circular ring
The moment of inertia of a circular ring rotating about an axis passing through its center and perpendicular to its plane is given by the formula:
I = 0.5 * m * r^2
where,
m = mass of the circular ring
r = radius of the circular ring
Substituting the values, we get:
I = 0.5 * 1 kg * (0.2 m)^2
I = 0.02 kg.m^2
Step 3: Calculate the angular velocity (ω) of the circular ring
Angular velocity (ω) is given by the formula:
ω = 2πf
where,
f = frequency of rotation
Substituting the values, we get:
ω = 2 * 3.14 * 10 rad/s
ω = 62.8 rad/s
Step 4: Calculate the angular momentum (L) of the circular ring
Using the formula L = Iω, we can calculate the angular momentum:
L = 0.02 kg.m^2 * 62.8 rad/s
L = 1.256 kg.m^2/s
Answer:
The angular momentum of the circular ring about its axis of rotation is 1.256 kg.m^2/s.
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A circular ring of diameter 40cm and mass 1kg is rotating about an axis normal to its plane and passing through the centre with a frequency of 10 rotations per second. Calculate the angular momentum about its axis of rotation?
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A circular ring of diameter 40cm and mass 1kg is rotating about an axis normal to its plane and passing through the centre with a frequency of 10 rotations per second. Calculate the angular momentum about its axis of rotation? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A circular ring of diameter 40cm and mass 1kg is rotating about an axis normal to its plane and passing through the centre with a frequency of 10 rotations per second. Calculate the angular momentum about its axis of rotation? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A circular ring of diameter 40cm and mass 1kg is rotating about an axis normal to its plane and passing through the centre with a frequency of 10 rotations per second. Calculate the angular momentum about its axis of rotation?.
A circular ring of diameter 40cm and mass 1kg is rotating about an axis normal to its plane and passing through the centre with a frequency of 10 rotations per second. Calculate the angular momentum about its axis of rotation? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A circular ring of diameter 40cm and mass 1kg is rotating about an axis normal to its plane and passing through the centre with a frequency of 10 rotations per second. Calculate the angular momentum about its axis of rotation? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A circular ring of diameter 40cm and mass 1kg is rotating about an axis normal to its plane and passing through the centre with a frequency of 10 rotations per second. Calculate the angular momentum about its axis of rotation?.
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