The moment of inertia in rotational motion is equivalent to :

Options

A. (a)angular velocity of linear motion
B. (b)mass of linear motion
C. (c)frequency of linear motion
D. (d)current

Answer

To solve the question regarding what the moment of inertia in rotational motion is equivalent to, we can follow these steps:

### Step 1: Understand the Concept of Moment of Inertia
The moment of inertia (I) is a measure of an object's resistance to changes in its rotation. It depends on the mass distribution of the object relative to the axis of rotation.

### Step 2: Relate Moment of Inertia to Linear Motion
In linear motion, the equivalent concept to moment of inertia is mass (m). Just as mass quantifies an object's resistance to linear acceleration, the moment of inertia quantifies an object's resistance to angular acceleration.

### Step 3: Identify the Key Equations
In linear motion, the relationship between force (F), mass (m), and acceleration (a) is given by Newton's second law:
\[ F = m \cdot a \]

In rotational motion, the equivalent relationship involves torque (τ), moment of inertia (I), and angular acceleration (α):
\[ τ = I \cdot α \]

### Step 4: Draw Comparisons
- Linear motion: Mass (m) is the resistance to linear acceleration (a).
- Rotational motion: Moment of inertia (I) is the resistance to angular acceleration (α).

### Step 5: Conclusion
From the comparisons, we can conclude that the moment of inertia (I) in rotational motion is equivalent to mass (m) in linear motion.

### Final Answer
The moment of inertia in rotational motion is equivalent to mass in linear motion.

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