The graph between the angular momentum J and angular velocity `omega` will be :-

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Answer

To find the relationship between angular momentum \( J \) and angular velocity \( \omega \), we can follow these steps:

### Step 1: Understand the Formula for Angular Momentum
The angular momentum \( J \) of a rotating object is given by the formula:
\[ J = I \cdot \omega \]
where \( I \) is the moment of inertia and \( \omega \) is the angular velocity.

### Step 2: Identify the Variables
In this equation:
- \( J \) (angular momentum) is the dependent variable.
- \( \omega \) (angular velocity) is the independent variable.
- \( I \) (moment of inertia) is a constant for a given object.

### Step 3: Rearranging the Equation
The equation can be rearranged to express \( J \) in terms of \( \omega \):
\[ J = I \cdot \omega \]
This indicates that \( J \) is directly proportional to \( \omega \).

### Step 4: Graphing the Relationship
To graph this relationship:
- Let \( J \) be on the y-axis and \( \omega \) be on the x-axis.
- The equation \( J = I \cdot \omega \) is in the form of \( y = mx \), where:
- \( y \) is \( J \),
- \( x \) is \( \omega \),
- \( m \) (the slope) is \( I \), and
- there is no y-intercept (c = 0).

### Step 5: Conclusion about the Graph
Since the graph passes through the origin (0,0) and has a slope equal to the moment of inertia \( I \), the graph between angular momentum \( J \) and angular velocity \( \omega \) will be a straight line through the origin.

### Final Answer
The graph between angular momentum \( J \) and angular velocity \( \omega \) is a straight line passing through the origin.

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