16 Constanta I Eeriodis Table A force Fof magnitude F making an angle e with the x axis is applied to a particle located along axis of rotation A, at Cartesian coordinates (0,0) in the figure. The vector Flies in the xy plane, and the four axes of rotation A, B. C, and D all lie perpendicular to the xy plane. (Eigure 1) A particle is located at a vector postion i with respect to an axis of rotation (thus F points from the axis to the point at which the particle is located). The magnitude of the torque r about this axis due to a force Facting on the particle is given by T rF sin(a)- (moment arm)- FrF where a is the angle between F and F,r is the magnitude of F, Fis the magnitude of F, the component of i that is perpendicular to Fis the moment arm, and F, is the component of the force that is perpendicular to F. Sign convention: You will need to determine the sign by analyzing the direction of the rotation that the torgue would tend to produce. Recal that negative torque about an axis coresponds to clockwise rotation. In this problem, you must express the angle a in the above equation in terms of 6. 6, andior when entering your answers. Keep in mind that T= 180 degrees and (x/2) = 90 degrees. What is the torque TA about axis A due to the force F? Express the torque about axis A at Cartesian coordinates (0, 0). > View Available Hintis) * O E ? Submit What is the torque Tn about axis B due to the force F? (B is the point at Cartesian coordinates (0, 6), located a distance b trom the origin along the y axis.) Express the torque about axis B in terms of F, 0, o, 7, andior other given coordinate data. > View Available Hintis) V AE4 Ta = Submit • Part C Figure What is the torque te about axis C due to F? (C is the point at Cartesian coordinates (c, 0), a distance calong the x axis.) Express the torque about axis C in terms of F. 8, d. T. andior other given coordinate data. >View Available Hintis) V AE * O a ?
16 Constanta I Eeriodis Table A force Fof magnitude F making an angle e with the x axis is applied to a particle located along axis of rotation A, at Cartesian coordinates (0,0) in the figure. The vector Flies in the xy plane, and the four axes of rotation A, B. C, and D all lie perpendicular to the xy plane. (Eigure 1) A particle is located at a vector postion i with respect to an axis of rotation (thus F points from the axis to the point at which the particle is located). The magnitude of the torque r about this axis due to a force Facting on the particle is given by T rF sin(a)- (moment arm)- FrF where a is the angle between F and F,r is the magnitude of F, Fis the magnitude of F, the component of i that is perpendicular to Fis the moment arm, and F, is the component of the force that is perpendicular to F. Sign convention: You will need to determine the sign by analyzing the direction of the rotation that the torgue would tend to produce. Recal that negative torque about an axis coresponds to clockwise rotation. In this problem, you must express the angle a in the above equation in terms of 6. 6, andior when entering your answers. Keep in mind that T= 180 degrees and (x/2) = 90 degrees. What is the torque TA about axis A due to the force F? Express the torque about axis A at Cartesian coordinates (0, 0). > View Available Hintis) * O E ? Submit What is the torque Tn about axis B due to the force F? (B is the point at Cartesian coordinates (0, 6), located a distance b trom the origin along the y axis.) Express the torque about axis B in terms of F, 0, o, 7, andior other given coordinate data. > View Available Hintis) V AE4 Ta = Submit • Part C Figure What is the torque te about axis C due to F? (C is the point at Cartesian coordinates (c, 0), a distance calong the x axis.) Express the torque about axis C in terms of F. 8, d. T. andior other given coordinate data. >View Available Hintis) V AE * O a ?
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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This problem needed two photos. Thanks!
![**Torque and Rotation**
A particle is located at a vector position **r** with respect to an axis of rotation (thus **r** points from the axis to the point at which the particle is located). The magnitude of the torque **τ** about this axis due to a force **F⃗** acting on the particle is given by:
\[ τ = rF \sin(ϕ) = (\text{moment arm}) \cdot F = r_{\perp}F_{\perp} \]
where ϕ is the angle between **r** and **F⃗**, r is the magnitude of **r**, F is the magnitude of **F⃗**, r⊥ is the moment arm, and F⊥ is the component of the force that is perpendicular to **r**.
**Sign Convention:**
You will need to determine the sign by analyzing the direction of the rotation that the torque would tend to produce. Recall that negative torque about an axis corresponds to clockwise rotation.
In this problem, you must express the angle ϕ in terms of θ, ϕ, and/or when entering your answers. Keep in mind that π = 180 degrees and (π/2) = 90 degrees.
**Part A**
What is the torque τA about axis A due to the force **F⃗**?
*Express the torque about axis A at Cartesian coordinates (0, 0).*
\[ τ_{A} = \]
**Part B**
What is the torque τB about axis B due to the force **F⃗**? (B is the point at Cartesian coordinates (0, b), located a distance b from the origin along the y-axis.)
*Express the torque about axis B in terms of F, θ, ϕ, π, and/or other given coordinate data.*
\[ τ_{B} = \]
**Part C**
What is the torque τC about axis C due to **F⃗**? (C is the point at Cartesian coordinates (c, 0), a distance c along the x-axis.)
*Express the torque about axis C in terms of F, θ, ϕ, π, and/or other given coordinate data.*
\[ τ_{C} = \]
**Figure Description:**
- The figure shows a coordinate system with the x and y axes.
- Points A, B, C, and D are marked with their respective axes perpendicular to the](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9f8ea0c3-20cc-4167-a0d0-5d27a7bf8fa1%2F1a686785-4d31-4427-bde9-aba7b54c8ece%2Fg9f5grt_processed.png&w=3840&q=75)
Transcribed Image Text:**Torque and Rotation**
A particle is located at a vector position **r** with respect to an axis of rotation (thus **r** points from the axis to the point at which the particle is located). The magnitude of the torque **τ** about this axis due to a force **F⃗** acting on the particle is given by:
\[ τ = rF \sin(ϕ) = (\text{moment arm}) \cdot F = r_{\perp}F_{\perp} \]
where ϕ is the angle between **r** and **F⃗**, r is the magnitude of **r**, F is the magnitude of **F⃗**, r⊥ is the moment arm, and F⊥ is the component of the force that is perpendicular to **r**.
**Sign Convention:**
You will need to determine the sign by analyzing the direction of the rotation that the torque would tend to produce. Recall that negative torque about an axis corresponds to clockwise rotation.
In this problem, you must express the angle ϕ in terms of θ, ϕ, and/or when entering your answers. Keep in mind that π = 180 degrees and (π/2) = 90 degrees.
**Part A**
What is the torque τA about axis A due to the force **F⃗**?
*Express the torque about axis A at Cartesian coordinates (0, 0).*
\[ τ_{A} = \]
**Part B**
What is the torque τB about axis B due to the force **F⃗**? (B is the point at Cartesian coordinates (0, b), located a distance b from the origin along the y-axis.)
*Express the torque about axis B in terms of F, θ, ϕ, π, and/or other given coordinate data.*
\[ τ_{B} = \]
**Part C**
What is the torque τC about axis C due to **F⃗**? (C is the point at Cartesian coordinates (c, 0), a distance c along the x-axis.)
*Express the torque about axis C in terms of F, θ, ϕ, π, and/or other given coordinate data.*
\[ τ_{C} = \]
**Figure Description:**
- The figure shows a coordinate system with the x and y axes.
- Points A, B, C, and D are marked with their respective axes perpendicular to the
![## Educational Content on Torque and Rotation
**Overview**
A force \( \vec{F} \) of magnitude \( F \) making an angle \( \theta \) with the x-axis is applied to a particle located along axis of rotation A, at Cartesian coordinates \( (0,0) \) in the figure. The vector \( \vec{F} \) lies in the xy plane, and the four axes of rotation A, B, C, and D are all perpendicular to the xy plane.
### Figure Description
The figure illustrates a coordinate system with an x-axis and y-axis. Four axes of rotation (A, B, C, and D) are marked, with a force vector \( \vec{F} \) making an angle \( \theta \) with the x-axis. The point A is at the origin \( (0,0) \), B is at coordinates \( (0, b) \) along the y-axis, C is at \( (c, 0) \) along the x-axis, and D is located a distance \( d \) from the origin, making an angle \( \phi \) with the x-axis. The direction of rotational motion is indicated by a circular arrow.
### Problem Components
#### Part A
What is the torque \( \tau_A \) about axis A due to the force \( \vec{F} \)?
- Express the torque about axis A in terms of \( F, \theta, r \), and/or other given coordinate data.
Input Box: \( \tau_A = \) [ ]
#### Part B
What is the torque \( \tau_B \) about axis B due to the force \( \vec{F} \)?
- B is the point at Cartesian coordinates \( (0, b) \), located a distance \( b \) from the origin along the y-axis.
- Express the torque about axis B in terms of \( F, b, \theta, r \), and/or other given coordinate data.
Input Box: \( \tau_B = \) [ ]
#### Part C
What is the torque \( \tau_C \) about axis C due to \( \vec{F} \)?
- C is the point at Cartesian coordinates \( (c, 0) \), a distance \( c \) along the x axis.
- Express the torque about axis C in terms of \( F, c, \theta, r \](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9f8ea0c3-20cc-4167-a0d0-5d27a7bf8fa1%2F1a686785-4d31-4427-bde9-aba7b54c8ece%2Fev83deb_processed.png&w=3840&q=75)
Transcribed Image Text:## Educational Content on Torque and Rotation
**Overview**
A force \( \vec{F} \) of magnitude \( F \) making an angle \( \theta \) with the x-axis is applied to a particle located along axis of rotation A, at Cartesian coordinates \( (0,0) \) in the figure. The vector \( \vec{F} \) lies in the xy plane, and the four axes of rotation A, B, C, and D are all perpendicular to the xy plane.
### Figure Description
The figure illustrates a coordinate system with an x-axis and y-axis. Four axes of rotation (A, B, C, and D) are marked, with a force vector \( \vec{F} \) making an angle \( \theta \) with the x-axis. The point A is at the origin \( (0,0) \), B is at coordinates \( (0, b) \) along the y-axis, C is at \( (c, 0) \) along the x-axis, and D is located a distance \( d \) from the origin, making an angle \( \phi \) with the x-axis. The direction of rotational motion is indicated by a circular arrow.
### Problem Components
#### Part A
What is the torque \( \tau_A \) about axis A due to the force \( \vec{F} \)?
- Express the torque about axis A in terms of \( F, \theta, r \), and/or other given coordinate data.
Input Box: \( \tau_A = \) [ ]
#### Part B
What is the torque \( \tau_B \) about axis B due to the force \( \vec{F} \)?
- B is the point at Cartesian coordinates \( (0, b) \), located a distance \( b \) from the origin along the y-axis.
- Express the torque about axis B in terms of \( F, b, \theta, r \), and/or other given coordinate data.
Input Box: \( \tau_B = \) [ ]
#### Part C
What is the torque \( \tau_C \) about axis C due to \( \vec{F} \)?
- C is the point at Cartesian coordinates \( (c, 0) \), a distance \( c \) along the x axis.
- Express the torque about axis C in terms of \( F, c, \theta, r \
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