A homogeneous disc of mass 2 kg and radius 15 cm is rotating about its axis with an angular velocity of 4 rad/s. the linear momentum of the disc is

Options

A. 1.2 kg m/s
B. 1.0 kg m/s
C. 0.6 kg m/s
D. zero

Explanation

To find the linear momentum of a homogeneous disc rotating about its axis, we can follow these steps:

### Step 1: Understand the given data
- Mass of the disc (m) = 2 kg
- Radius of the disc (r) = 15 cm = 0.15 m (convert cm to m)
- Angular velocity (ω) = 4 rad/s

### Step 2: Calculate the moment of inertia (I) of the disc
The moment of inertia (I) for a homogeneous disc about its axis is given by the formula:
\[ I = \frac{1}{2} m r^2 \]
Substituting the values:
\[ I = \frac{1}{2} \times 2 \, \text{kg} \times (0.15 \, \text{m})^2 \]
\[ I = \frac{1}{2} \times 2 \times 0.0225 \]
\[ I = 0.0225 \, \text{kg m}^2 \]

### Step 3: Calculate the angular momentum (J)
The angular momentum (J) can be calculated using the formula:
\[ J = I \cdot \omega \]
Substituting the values:
\[ J = 0.0225 \, \text{kg m}^2 \times 4 \, \text{rad/s} \]
\[ J = 0.09 \, \text{kg m}^2/\text{s} \]

### Step 4: Relate angular momentum to linear momentum
The relationship between angular momentum (J) and linear momentum (P) is given by:
\[ J = P \cdot r \]
From this, we can express linear momentum (P) as:
\[ P = \frac{J}{r} \]
Substituting the values:
\[ P = \frac{0.09 \, \text{kg m}^2/\text{s}}{0.15 \, \text{m}} \]
\[ P = 0.6 \, \text{kg m/s} \]

### Final Answer
The linear momentum of the disc is:
\[ P = 0.6 \, \text{kg m/s} \]

---