A symmetrical body of mass M and radius R is rolling without slipping on a horizontal surface with linear speed v. Then its angular speed is

Options

A. v/R
B. Continuously increasing
C. Dependent on mass M
D. Independent of radius (R)

Answer

To solve the problem of finding the angular speed (ω) of a symmetrical body of mass M and radius R that is rolling without slipping on a horizontal surface with a linear speed (v), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Rolling Without Slipping**:
- When a body rolls without slipping, the point of contact with the ground does not slide. This means that the linear speed of the center of mass (v) is related to the angular speed (ω) of the body.

2. **Using the Relationship Between Linear Speed and Angular Speed**:
- The relationship between the linear speed (v) of the center of mass and the angular speed (ω) can be expressed as:
\[ v = R \cdot \omega \]
- Here, R is the radius of the body.

3. **Rearranging the Equation to Solve for Angular Speed**:
- To find the angular speed (ω), we can rearrange the equation:
\[ \omega = \frac{v}{R} \]

4. **Conclusion**:
- Therefore, the angular speed (ω) of the symmetrical body is given by:
\[ \omega = \frac{v}{R} \]

### Final Answer:
The angular speed of the body is \( \frac{v}{R} \).

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