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A wheel rotating at an angular speed of 20 rad/s is brought to rest by a constant torque in 4.0 seconds. If the moment of inertia of the wheel about the axis of rotation is 0.20find the work done by the torque in the first two seconds.?
Most Upvoted Answer
A wheel rotating at an angular speed of 20 rad/s is brought to rest by...
Let a = angular acceleration
a = (0 - 20)/4 = -5 rad/s²
Torque T = Ia where I = moment of inertia
=> T = (0.2)(5) = 1
Angular displacement in 2 sec,s = wt - at²/2 = 40 - 10 = 30
Work done = T x s = 30 J
a = (0 - 20)/4 = -5 rad/s²
Torque T = Ia where I = moment of inertia
=> T = (0.2)(5) = 1
Angular displacement in 2 sec,s = wt - at²/2 = 40 - 10 = 30
Work done = T x s = 30 J
Community Answer
A wheel rotating at an angular speed of 20 rad/s is brought to rest by...
Given:
To Find:
Explanation:
The formula for the torque required to bring the wheel to rest from an angular speed ω is given by:
τ = Iα
where τ is the torque, I is the moment of inertia of the wheel, and α is the angular acceleration of the wheel.
The formula for angular acceleration is given by:
α = (ω - ω0)/t
where ω0 is the initial angular speed, which is 20 rad/s in this case.
Substituting the values in the above formulas, we get:
α = (20 - 0)/4.0 = 5 rad/s²
τ = Iα = 0.20 × 5 = 1 Nm
The work done by the torque in the first two seconds is given by:
W(0-2) = τθ
where θ is the angle rotated by the wheel in the first two seconds.
The formula for the angle rotated by the wheel is given by:
θ = ω0t + (1/2)αt²
Substituting the values in the above formula, we get:
θ = 20 × 2 + (1/2) × 5 × (2)² = 30 rad
Substituting the values in the formula for work done, we get:
W(0-2) = 1 × 30 = 30 J
Therefore, the work done by the torque in the first two seconds is 30 J.
Answer: The work done by the torque in the first two seconds is 30 J.
- Angular speed of the wheel, ω = 20 rad/s
- Time taken to bring the wheel to rest, t = 4.0 s
- Moment of inertia of the wheel, I = 0.20
To Find:
- Work done by the torque in the first two seconds, W(0-2)
Explanation:
The formula for the torque required to bring the wheel to rest from an angular speed ω is given by:
τ = Iα
where τ is the torque, I is the moment of inertia of the wheel, and α is the angular acceleration of the wheel.
The formula for angular acceleration is given by:
α = (ω - ω0)/t
where ω0 is the initial angular speed, which is 20 rad/s in this case.
Substituting the values in the above formulas, we get:
α = (20 - 0)/4.0 = 5 rad/s²
τ = Iα = 0.20 × 5 = 1 Nm
The work done by the torque in the first two seconds is given by:
W(0-2) = τθ
where θ is the angle rotated by the wheel in the first two seconds.
The formula for the angle rotated by the wheel is given by:
θ = ω0t + (1/2)αt²
Substituting the values in the above formula, we get:
θ = 20 × 2 + (1/2) × 5 × (2)² = 30 rad
Substituting the values in the formula for work done, we get:
W(0-2) = 1 × 30 = 30 J
Therefore, the work done by the torque in the first two seconds is 30 J.
Answer: The work done by the torque in the first two seconds is 30 J.
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A wheel rotating at an angular speed of 20 rad/s is brought to rest by a constant torque in 4.0 seconds. If the moment of inertia of the wheel about the axis of rotation is 0.20find the work done by the torque in the first two seconds.?
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A wheel rotating at an angular speed of 20 rad/s is brought to rest by a constant torque in 4.0 seconds. If the moment of inertia of the wheel about the axis of rotation is 0.20find the work done by the torque in the first two seconds.? 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 wheel rotating at an angular speed of 20 rad/s is brought to rest by a constant torque in 4.0 seconds. If the moment of inertia of the wheel about the axis of rotation is 0.20find the work done by the torque in the first two seconds.? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A wheel rotating at an angular speed of 20 rad/s is brought to rest by a constant torque in 4.0 seconds. If the moment of inertia of the wheel about the axis of rotation is 0.20find the work done by the torque in the first two seconds.?.
A wheel rotating at an angular speed of 20 rad/s is brought to rest by a constant torque in 4.0 seconds. If the moment of inertia of the wheel about the axis of rotation is 0.20find the work done by the torque in the first two seconds.? 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 wheel rotating at an angular speed of 20 rad/s is brought to rest by a constant torque in 4.0 seconds. If the moment of inertia of the wheel about the axis of rotation is 0.20find the work done by the torque in the first two seconds.? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A wheel rotating at an angular speed of 20 rad/s is brought to rest by a constant torque in 4.0 seconds. If the moment of inertia of the wheel about the axis of rotation is 0.20find the work done by the torque in the first two seconds.?.
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