For rotational motion, the Newton's second law of motion is indicated by :-

Options

A. `omega_(1)^(2)+2alpha theta`
B. `vecF=(d vecp)/(dt)`
C. `vec tau=(d vecJ)/(dt) `
D. `vecF_(12)=vecF_(21)`

Answer

To solve the question regarding how Newton's second law of motion is represented in rotational motion, we can follow these steps:

### Step-by-Step Solution:

1. **Understand Newton's Second Law**:
- In linear motion, Newton's second law states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. Mathematically, this is expressed as:
\[ F = m \cdot a \]

2. **Relate Linear Motion to Rotational Motion**:
- In rotational motion, we need to consider analogous quantities. The force \( F \) in linear motion corresponds to torque \( \tau \) in rotational motion. Similarly, mass \( m \) corresponds to the moment of inertia \( I \), and linear acceleration \( a \) corresponds to angular acceleration \( \alpha \).

3. **Write the Rotational Form of Newton's Second Law**:
- By substituting these analogous quantities into the linear form of Newton's second law, we get:
\[ \tau = I \cdot \alpha \]
- Here, \( \tau \) is the torque, \( I \) is the moment of inertia, and \( \alpha \) is the angular acceleration.

4. **Interpret the Equation**:
- This equation indicates that the net torque acting on a body is equal to the product of its moment of inertia and its angular acceleration. This is the rotational equivalent of Newton's second law.

5. **Identify the Correct Option**:
- If the question provides multiple-choice options, the correct choice would be the one that states:
\[ \tau = I \cdot \alpha \]
- This represents Newton's second law in the context of rotational motion.

### Conclusion:
Thus, for rotational motion, Newton's second law is indicated by the equation \( \tau = I \cdot \alpha \).

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