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Suppose a disc is rotating counter clock...

Suppose a disc is rotating counter clockwise in the plane of the paper then

A

It's angular velocity vector will be perpendicular to the page pointing up out of the page

B

It's angular velocity vector will be perpendicular to the page pointing inwards

C

It's angular velocity vector acts along the tangent to the disc.

D

none of the above is correct

Text Solution

AI Generated Solution

The correct Answer is:
To solve the question regarding the rotation of a disc in the plane of the paper, we need to analyze the situation step by step. ### Step-by-Step Solution: 1. **Understanding the Rotation Direction**: - The disc is rotating counterclockwise. This means that if you were to look down at the disc from above, it would be spinning in the opposite direction to the movement of the hands of a clock. 2. **Identifying the Angular Velocity Vector**: - The angular velocity vector (\( \vec{\omega} \)) is a vector that describes the axis of rotation and the speed of rotation. By the right-hand rule, if you curl the fingers of your right hand in the direction of the rotation (counterclockwise), your thumb will point in the direction of the angular velocity vector. 3. **Applying the Right-Hand Rule**: - For a counterclockwise rotation, when you apply the right-hand rule, your thumb points upwards, out of the plane of the paper. This indicates that the angular velocity vector is directed out of the page. 4. **Evaluating the Given Options**: - **Option 1**: "Its angular velocity will be perpendicular to the page pointing up out of the page." This is correct based on our analysis. - **Option 2**: "Its angular velocity will be perpendicular to the page pointing inwards." This is incorrect because the angular velocity points outwards. - **Option 3**: "Its angular velocity vector acts along the tangent to the disk." This is incorrect as the angular velocity vector is not tangent but rather perpendicular to the plane of rotation. - **Option 4**: "None of the above." This is incorrect since we have identified a correct option. 5. **Conclusion**: - The correct statement is Option 1: "Its angular velocity will be perpendicular to the page pointing up out of the page." ### Final Answer: The correct option is **Option 1**. ---
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