If there is change of angular momentum from 1 J to 4 J in 4 second, then the torque is

Options

A. `(3//4)J`
B. 1 J
C. (5//4)J
D. (4//3)J

Answer

To solve the problem of finding the torque given the change in angular momentum, we can follow these steps:

### Step 1: Understand the given values
We are given:
- Initial angular momentum (Li) = 1 J·s (joule-second)
- Final angular momentum (Lf) = 4 J·s (joule-second)
- Time interval (Δt) = 4 seconds

### Step 2: Calculate the change in angular momentum
The change in angular momentum (ΔL) can be calculated using the formula:
\[ \Delta L = L_f - L_i \]
Substituting the values:
\[ \Delta L = 4 \, \text{J·s} - 1 \, \text{J·s} = 3 \, \text{J·s} \]

### Step 3: Use the relationship between torque and angular momentum
The average torque (τ) is defined as the rate of change of angular momentum with respect to time:
\[ \tau = \frac{\Delta L}{\Delta t} \]

### Step 4: Substitute the values into the torque formula
Now, substituting the values we have:
\[ \tau = \frac{3 \, \text{J·s}}{4 \, \text{s}} = \frac{3}{4} \, \text{J·s/s} = 0.75 \, \text{N·m} \]

### Final Answer
Thus, the torque is:
\[ \tau = 0.75 \, \text{N·m} \]

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