list the force equations for the rotation mass m ( horizontal direction x and vertical direction y) , and force equation for hanging mass M. find the time for m to complete one circle (period).

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Chapter1: Units, Trigonometry. And Vectors
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list the force equations for the rotation mass m ( horizontal direction x and vertical direction y) , and force equation for hanging mass M. find the time for m to complete one circle (period). 

The diagram depicts a physical system involving a pulley with a mass. It consists of the following components:

1. **Pulley System**: 
   - There are two circular objects indicated as \( O_1 \) and \( O_2 \). 
   - \( O_1 \) is fixed at the origin, and \( O_2 \) is a point on the circular path of the pulley.

2. **Masses**:
   - A small mass \( m \) is located at \( O_1 \).
   - A larger mass \( M \) is suspended and connected to the system by a string or rigid connector that passes over the pulley.

3. **Angle and Radius**:
   - \( \theta \) is the angle between the horizontal line \( O_1O_2 \) and the radius \( R \). This angle is marked by a dashed line showing the direction of the radius from \( O_1 \) to \( O_2 \).

4. **Axes**:
   - The \( x \)-axis is horizontal, and the \( y \)-axis is vertical, intersecting at point \( O_1 \).

This schematic can be used to analyze forces, kinematics, or energy systems in mechanics, often applied to problems involving rotational motion or pendulum dynamics.
Transcribed Image Text:The diagram depicts a physical system involving a pulley with a mass. It consists of the following components: 1. **Pulley System**: - There are two circular objects indicated as \( O_1 \) and \( O_2 \). - \( O_1 \) is fixed at the origin, and \( O_2 \) is a point on the circular path of the pulley. 2. **Masses**: - A small mass \( m \) is located at \( O_1 \). - A larger mass \( M \) is suspended and connected to the system by a string or rigid connector that passes over the pulley. 3. **Angle and Radius**: - \( \theta \) is the angle between the horizontal line \( O_1O_2 \) and the radius \( R \). This angle is marked by a dashed line showing the direction of the radius from \( O_1 \) to \( O_2 \). 4. **Axes**: - The \( x \)-axis is horizontal, and the \( y \)-axis is vertical, intersecting at point \( O_1 \). This schematic can be used to analyze forces, kinematics, or energy systems in mechanics, often applied to problems involving rotational motion or pendulum dynamics.
Expert Solution
Step 1: Given

Mass of hanging object = M 

Mass of rotating object = m 

Radius of circle = R 

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