Find the net torque on the wheel in the figure below about the axle through O perpendicular to the page, taking a = 13.0 cm and b = 31.0 cm. (Indicate the direction with the sign of your answer. Assume that the positive direction is counterclockwise.)

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Chapter1: Units, Trigonometry. And Vectors
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**Problem Statement:**

Find the net torque on the wheel in the figure below about the axle through O perpendicular to the page, taking \(a = 13.0 \, \text{cm}\) and \(b = 31.0 \, \text{cm}\). (Indicate the direction with the sign of your answer. Assume that the positive direction is counterclockwise.)

**Diagram Explanation:**

- The diagram shows a wheel with forces acting at different points:
  - A force of \(30.0 \, \text{N}\) is applied at an angle \(\theta\), acting upwards from the center O at radius \(b\).
  - A force of \(12.0 \, \text{N}\) acts counterclockwise on the left side of the wheel at radius \(a\).
  - A force of \(10.0 \, \text{N}\) acts to the right at the perimeter of the wheel.
  - A force of \(9.0 \, \text{N}\) acts downward on the far right side at radius \(b\).

**Units:**

- Torque is measured in \(\text{N} \cdot \text{m}\).

**Considerations:**

- Calculate each torque component separately, considering direction (counterclockwise is positive).
- The torque \(\tau\) is given by \(\tau = r \cdot F \cdot \sin(\theta)\), where \(r\) is the radius, \(F\) is the force, and \(\theta\) is the angle between the force and the lever arm. Adjust the formula based on given or needed angles.
Transcribed Image Text:**Problem Statement:** Find the net torque on the wheel in the figure below about the axle through O perpendicular to the page, taking \(a = 13.0 \, \text{cm}\) and \(b = 31.0 \, \text{cm}\). (Indicate the direction with the sign of your answer. Assume that the positive direction is counterclockwise.) **Diagram Explanation:** - The diagram shows a wheel with forces acting at different points: - A force of \(30.0 \, \text{N}\) is applied at an angle \(\theta\), acting upwards from the center O at radius \(b\). - A force of \(12.0 \, \text{N}\) acts counterclockwise on the left side of the wheel at radius \(a\). - A force of \(10.0 \, \text{N}\) acts to the right at the perimeter of the wheel. - A force of \(9.0 \, \text{N}\) acts downward on the far right side at radius \(b\). **Units:** - Torque is measured in \(\text{N} \cdot \text{m}\). **Considerations:** - Calculate each torque component separately, considering direction (counterclockwise is positive). - The torque \(\tau\) is given by \(\tau = r \cdot F \cdot \sin(\theta)\), where \(r\) is the radius, \(F\) is the force, and \(\theta\) is the angle between the force and the lever arm. Adjust the formula based on given or needed angles.
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