In the above question, the change in angular momentum of disc in first 2 seconds in Nm second will be:

Options

A. 2.5
B. 5
C. 10
D. 20

Answer

To find the change in angular momentum of the disc in the first 2 seconds, we can follow these steps:

### Step 1: Identify the given values
- Moment of inertia (I) of the disc = 2 kg·m²
- Final angular velocity (ω_f) at t = 2 seconds = 5 rad/s
- Initial angular velocity (ω_i) = 0 rad/s (since the system starts from rest)

### Step 2: Write the formula for angular momentum
The angular momentum (L) of a rotating object is given by the formula:
\[ L = I \cdot \omega \]
where:
- L = angular momentum
- I = moment of inertia
- ω = angular velocity

### Step 3: Calculate the final angular momentum (L_f)
Using the final angular velocity (ω_f):
\[ L_f = I \cdot \omega_f \]
Substituting the values:
\[ L_f = 2 \, \text{kg·m²} \cdot 5 \, \text{rad/s} = 10 \, \text{kg·m²/s} \]

### Step 4: Calculate the initial angular momentum (L_i)
Using the initial angular velocity (ω_i):
\[ L_i = I \cdot \omega_i \]
Substituting the values:
\[ L_i = 2 \, \text{kg·m²} \cdot 0 \, \text{rad/s} = 0 \, \text{kg·m²/s} \]

### Step 5: Calculate the change in angular momentum (ΔL)
The change in angular momentum (ΔL) is given by:
\[ \Delta L = L_f - L_i \]
Substituting the values:
\[ \Delta L = 10 \, \text{kg·m²/s} - 0 \, \text{kg·m²/s} = 10 \, \text{kg·m²/s} \]

### Step 6: Convert the units to Newton meter
Since 1 kg·m²/s is equivalent to 1 Nm, we have:
\[ \Delta L = 10 \, \text{Nm} \]

### Final Answer
The change in angular momentum of the disc in the first 2 seconds is **10 Nm**.

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