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A wheel of 1.2 diameter is mounted on a shaft between two bearings. The wheel is set rotating from rest by applying a constant moment of 110Nm at the rim amd the speed of the wheel becomes 100rpm within 10 mins from rest. Determine a) the number of revolutions made by the wheel during this time b) the angular acceleration of the wheel c) the work done in rotating the wheel during this time d) peripheral velocity of the wheel at 100rpm?
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A wheel of 1.2 diameter is mounted on a shaft between two bearings. Th...
**a) Number of Revolutions Made by the Wheel**
To determine the number of revolutions made by the wheel during the given time, we need to convert the time from minutes to seconds and then calculate the angular displacement.
Given:
- Diameter of the wheel = 1.2 meters
- Radius of the wheel (r) = diameter/2 = 1.2/2 = 0.6 meters
- Moment applied at the rim (M) = 110 Nm
- Speed of the wheel (ω) = 100 rpm
- Time (t) = 10 minutes
First, let's convert the time to seconds:
10 minutes = 10 * 60 seconds = 600 seconds
To calculate the number of revolutions, we need to find the angular displacement of the wheel. The formula to relate angular displacement (θ) with angular velocity (ω) and time (t) is:
θ = ω * t
Substituting the given values:
θ = (100 rpm) * (2π radians/1 minute) * (10 minutes) = 2000π radians
Since one revolution is equal to 2π radians, we can calculate the number of revolutions (N) as:
N = θ / (2π) = (2000π radians) / (2π radians/revolution) = 1000 revolutions
Therefore, the wheel makes 1000 revolutions during the given time.
**b) Angular Acceleration of the Wheel**
To determine the angular acceleration of the wheel, we need to use the formula that relates angular acceleration (α) with angular velocity (ω) and time (t):
α = (ωf - ωi) / t
Given:
- Initial angular velocity (ωi) = 0 rpm (as the wheel starts from rest)
- Final angular velocity (ωf) = 100 rpm
- Time (t) = 10 minutes = 600 seconds
Converting the angular velocities to radians per second:
ωi = 0 rpm * (2π radians/1 minute) = 0 rad/s
ωf = 100 rpm * (2π radians/1 minute) = 200π rad/s
Substituting the values into the formula:
α = (200π rad/s - 0 rad/s) / 600 s = (200π / 600) rad/s² = (π / 3) rad/s²
Therefore, the angular acceleration of the wheel is π/3 rad/s².
**c) Work Done in Rotating the Wheel**
The work done in rotating the wheel can be calculated using the formula:
Work (W) = Moment (M) * Angular displacement (θ)
Given:
- Moment applied at the rim (M) = 110 Nm
- Angular displacement (θ) = 2000π radians
Substituting the values into the formula:
W = 110 Nm * 2000π radians = 220000π Nm
Therefore, the work done in rotating the wheel during the given time is 220000π Nm.
**d) Peripheral Velocity of the Wheel at 100rpm**
The peripheral velocity of a rotating object is the linear speed at its rim. It can be calculated using the formula:
Peripheral velocity (v) = Angular velocity (ω) * Radius (r)
Given:
- Angular velocity (ω) = 100 rpm
To determine the number of revolutions made by the wheel during the given time, we need to convert the time from minutes to seconds and then calculate the angular displacement.
Given:
- Diameter of the wheel = 1.2 meters
- Radius of the wheel (r) = diameter/2 = 1.2/2 = 0.6 meters
- Moment applied at the rim (M) = 110 Nm
- Speed of the wheel (ω) = 100 rpm
- Time (t) = 10 minutes
First, let's convert the time to seconds:
10 minutes = 10 * 60 seconds = 600 seconds
To calculate the number of revolutions, we need to find the angular displacement of the wheel. The formula to relate angular displacement (θ) with angular velocity (ω) and time (t) is:
θ = ω * t
Substituting the given values:
θ = (100 rpm) * (2π radians/1 minute) * (10 minutes) = 2000π radians
Since one revolution is equal to 2π radians, we can calculate the number of revolutions (N) as:
N = θ / (2π) = (2000π radians) / (2π radians/revolution) = 1000 revolutions
Therefore, the wheel makes 1000 revolutions during the given time.
**b) Angular Acceleration of the Wheel**
To determine the angular acceleration of the wheel, we need to use the formula that relates angular acceleration (α) with angular velocity (ω) and time (t):
α = (ωf - ωi) / t
Given:
- Initial angular velocity (ωi) = 0 rpm (as the wheel starts from rest)
- Final angular velocity (ωf) = 100 rpm
- Time (t) = 10 minutes = 600 seconds
Converting the angular velocities to radians per second:
ωi = 0 rpm * (2π radians/1 minute) = 0 rad/s
ωf = 100 rpm * (2π radians/1 minute) = 200π rad/s
Substituting the values into the formula:
α = (200π rad/s - 0 rad/s) / 600 s = (200π / 600) rad/s² = (π / 3) rad/s²
Therefore, the angular acceleration of the wheel is π/3 rad/s².
**c) Work Done in Rotating the Wheel**
The work done in rotating the wheel can be calculated using the formula:
Work (W) = Moment (M) * Angular displacement (θ)
Given:
- Moment applied at the rim (M) = 110 Nm
- Angular displacement (θ) = 2000π radians
Substituting the values into the formula:
W = 110 Nm * 2000π radians = 220000π Nm
Therefore, the work done in rotating the wheel during the given time is 220000π Nm.
**d) Peripheral Velocity of the Wheel at 100rpm**
The peripheral velocity of a rotating object is the linear speed at its rim. It can be calculated using the formula:
Peripheral velocity (v) = Angular velocity (ω) * Radius (r)
Given:
- Angular velocity (ω) = 100 rpm
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A wheel of 1.2 diameter is mounted on a shaft between two bearings. The wheel is set rotating from rest by applying a constant moment of 110Nm at the rim amd the speed of the wheel becomes 100rpm within 10 mins from rest. Determine a) the number of revolutions made by the wheel during this time b) the angular acceleration of the wheel c) the work done in rotating the wheel during this time d) peripheral velocity of the wheel at 100rpm?
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A wheel of 1.2 diameter is mounted on a shaft between two bearings. The wheel is set rotating from rest by applying a constant moment of 110Nm at the rim amd the speed of the wheel becomes 100rpm within 10 mins from rest. Determine a) the number of revolutions made by the wheel during this time b) the angular acceleration of the wheel c) the work done in rotating the wheel during this time d) peripheral velocity of the wheel at 100rpm? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A wheel of 1.2 diameter is mounted on a shaft between two bearings. The wheel is set rotating from rest by applying a constant moment of 110Nm at the rim amd the speed of the wheel becomes 100rpm within 10 mins from rest. Determine a) the number of revolutions made by the wheel during this time b) the angular acceleration of the wheel c) the work done in rotating the wheel during this time d) peripheral velocity of the wheel at 100rpm? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A wheel of 1.2 diameter is mounted on a shaft between two bearings. The wheel is set rotating from rest by applying a constant moment of 110Nm at the rim amd the speed of the wheel becomes 100rpm within 10 mins from rest. Determine a) the number of revolutions made by the wheel during this time b) the angular acceleration of the wheel c) the work done in rotating the wheel during this time d) peripheral velocity of the wheel at 100rpm?.
A wheel of 1.2 diameter is mounted on a shaft between two bearings. The wheel is set rotating from rest by applying a constant moment of 110Nm at the rim amd the speed of the wheel becomes 100rpm within 10 mins from rest. Determine a) the number of revolutions made by the wheel during this time b) the angular acceleration of the wheel c) the work done in rotating the wheel during this time d) peripheral velocity of the wheel at 100rpm? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A wheel of 1.2 diameter is mounted on a shaft between two bearings. The wheel is set rotating from rest by applying a constant moment of 110Nm at the rim amd the speed of the wheel becomes 100rpm within 10 mins from rest. Determine a) the number of revolutions made by the wheel during this time b) the angular acceleration of the wheel c) the work done in rotating the wheel during this time d) peripheral velocity of the wheel at 100rpm? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A wheel of 1.2 diameter is mounted on a shaft between two bearings. The wheel is set rotating from rest by applying a constant moment of 110Nm at the rim amd the speed of the wheel becomes 100rpm within 10 mins from rest. Determine a) the number of revolutions made by the wheel during this time b) the angular acceleration of the wheel c) the work done in rotating the wheel during this time d) peripheral velocity of the wheel at 100rpm?.
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A wheel of 1.2 diameter is mounted on a shaft between two bearings. The wheel is set rotating from rest by applying a constant moment of 110Nm at the rim amd the speed of the wheel becomes 100rpm within 10 mins from rest. Determine a) the number of revolutions made by the wheel during this time b) the angular acceleration of the wheel c) the work done in rotating the wheel during this time d) peripheral velocity of the wheel at 100rpm?, a detailed solution for A wheel of 1.2 diameter is mounted on a shaft between two bearings. The wheel is set rotating from rest by applying a constant moment of 110Nm at the rim amd the speed of the wheel becomes 100rpm within 10 mins from rest. Determine a) the number of revolutions made by the wheel during this time b) the angular acceleration of the wheel c) the work done in rotating the wheel during this time d) peripheral velocity of the wheel at 100rpm? has been provided alongside types of A wheel of 1.2 diameter is mounted on a shaft between two bearings. The wheel is set rotating from rest by applying a constant moment of 110Nm at the rim amd the speed of the wheel becomes 100rpm within 10 mins from rest. Determine a) the number of revolutions made by the wheel during this time b) the angular acceleration of the wheel c) the work done in rotating the wheel during this time d) peripheral velocity of the wheel at 100rpm? theory, EduRev gives you an
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