Find the net torque on the wheel in the figure below about the axle through O, taking a = 11.0 cm and b = 25.0 cm. (Assume that the positive direction is counterclockwise.) N.m 10.0 N 30.00 12.0 N 9.00 N

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**Problem Statement:**

Find the net torque on the wheel in the figure below about the axle through \( O \), taking \( a = 11.0 \, \text{cm} \) and \( b = 25.0 \, \text{cm} \). (Assume that the positive direction is counterclockwise.)

\[ \_\_\_\_\_\_ \, \text{N} \cdot \text{m} \]

**Diagram Explanation:**

The diagram is of a wheel with several forces acting on it at different points. The forces and relevant dimensions are labeled as follows:

1. There is a force of \( 12.0 \, \text{N} \) acting at an angle of \( 30.0^\circ \) above the horizontal to the left at the outer radius \( b \).
2. A force of \( 10.0 \, \text{N} \) is acting horizontally to the right at the outer radius \( b \).
3. A force of \( 9.00 \, \text{N} \) is acting vertically downward at the outer radius \( b \).

**Key Variables:**

- Radius \( a = 11.0 \, \text{cm} \)
- Radius \( b = 25.0 \, \text{cm} \)

The center of the wheel is marked as point \( O \).

**Diagram Elements:**

- The wheel has concentric circles indicating two distinct radii: \( a \) and \( b \).
- The forces are represented as vectors with specific magnitudes and directions.
- A dashed line indicates the angle \( 30.0^\circ \).

The problem requires calculating the net torque about point \( O \), considering the given forces and their respective angles and distances from the center. Counterclockwise torque is considered positive, and clockwise torque is considered negative.
Transcribed Image Text:**Problem Statement:** Find the net torque on the wheel in the figure below about the axle through \( O \), taking \( a = 11.0 \, \text{cm} \) and \( b = 25.0 \, \text{cm} \). (Assume that the positive direction is counterclockwise.) \[ \_\_\_\_\_\_ \, \text{N} \cdot \text{m} \] **Diagram Explanation:** The diagram is of a wheel with several forces acting on it at different points. The forces and relevant dimensions are labeled as follows: 1. There is a force of \( 12.0 \, \text{N} \) acting at an angle of \( 30.0^\circ \) above the horizontal to the left at the outer radius \( b \). 2. A force of \( 10.0 \, \text{N} \) is acting horizontally to the right at the outer radius \( b \). 3. A force of \( 9.00 \, \text{N} \) is acting vertically downward at the outer radius \( b \). **Key Variables:** - Radius \( a = 11.0 \, \text{cm} \) - Radius \( b = 25.0 \, \text{cm} \) The center of the wheel is marked as point \( O \). **Diagram Elements:** - The wheel has concentric circles indicating two distinct radii: \( a \) and \( b \). - The forces are represented as vectors with specific magnitudes and directions. - A dashed line indicates the angle \( 30.0^\circ \). The problem requires calculating the net torque about point \( O \), considering the given forces and their respective angles and distances from the center. Counterclockwise torque is considered positive, and clockwise torque is considered negative.
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