It torque is zero, then

Options

A. angular momentum is conserved
B. linear momentum is conserved
C. energy is conserved
D. angular momentum is not conserved

Explanation

To solve the question "If torque is zero, then...", we can analyze the implications of having zero torque on the system. Here are the steps to arrive at the correct answer:

### Step 1: Understand the Definition of Torque
Torque (\( \tau \)) is defined as the rate of change of angular momentum (\( L \)) with respect to time. Mathematically, it can be expressed as:
\[ \tau = \frac{dL}{dt} \]

### Step 2: Analyze the Given Condition
The question states that torque is zero:
\[ \tau = 0 \]
This implies that the rate of change of angular momentum is zero.

### Step 3: Deduce the Implication of Zero Torque
If the torque is zero, it means that:
\[ \frac{dL}{dt} = 0 \]
This indicates that the angular momentum \( L \) does not change with time, meaning it is constant.

### Step 4: Conclude About Angular Momentum
Since the angular momentum is constant when torque is zero, we can conclude that:
- Angular momentum is conserved.

### Step 5: Evaluate the Options
Now, we can evaluate the options given in the question:
1. Angular momentum is conserved (True, as derived).
2. Linear momentum is conserved (Not necessarily true; it depends on external forces).
3. Energy is conserved (Not necessarily true; it depends on the system).
4. Angular momentum is not conserved (False, as we established it is conserved).

### Final Answer
The correct answer is:
**Option 1: Angular momentum is conserved.**

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