If there is no external force acting on a nonrigid body, which of the followhng quantities must remain constant?

Options

A. angular momentum
B. linear momentum
C. kinetic energy
D. moment of inertia

Answer

To determine which quantities remain constant for a non-rigid body when no external forces are acting on it, we can analyze the situation step by step.

### Step 1: Understand the Concept of Conservation Laws
In physics, conservation laws state that certain quantities remain constant in an isolated system. For a body with no external forces acting on it, we need to identify which quantities are conserved.

**Hint:** Remember that conservation laws apply to quantities that are not influenced by external interactions.

### Step 2: Analyze Linear Momentum
Linear momentum (p) is defined as the product of mass (m) and velocity (v) of an object (p = mv). If there are no external forces acting on the body, the total linear momentum of the system must remain constant.

**Hint:** Think about how external forces can change the velocity of an object.

### Step 3: Analyze Angular Momentum
Angular momentum (L) is defined as the product of the moment of inertia (I) and angular velocity (ω) (L = Iω). If there are no external torques acting on the body, the total angular momentum of the system must also remain constant.

**Hint:** Consider how torques can influence the rotational motion of an object.

### Step 4: Consider Kinetic Energy
Kinetic energy (KE) is given by the formula KE = 1/2 mv² for translational motion and KE = 1/2 Iω² for rotational motion. In a non-rigid body, the internal structure can change, leading to energy transformations (e.g., some kinetic energy may convert to heat due to internal friction). Therefore, kinetic energy is not necessarily conserved.

**Hint:** Reflect on how internal movements and changes in structure can affect energy.

### Step 5: Evaluate Moment of Inertia
The moment of inertia (I) depends on the distribution of mass relative to the axis of rotation. For a non-rigid body, as the shape changes, the distance of mass elements from the center of mass changes, which means the moment of inertia can vary. Thus, it is not conserved.

**Hint:** Think about how the shape of an object can affect its moment of inertia.

### Conclusion
From the analysis:
- **Linear Momentum (Option 2)** remains constant.
- **Angular Momentum (Option 1)** remains constant.
- **Kinetic Energy (Option 3)** is not conserved due to internal changes.
- **Moment of Inertia (Option 4)** is not constant due to shape changes.

Thus, the correct answers are **Option 1 (Angular Momentum)** and **Option 2 (Linear Momentum)**.