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A disc of mass 1 kg and radius 10 cm is ...

A disc of mass 1 kg and radius 10 cm is rotating about its axis with an anuglar velocity of 2 rad/s. The linear momentum of the disc,

A

0.2 kg-m/s

B

zero

C

0.4 kg-m/s

D

0.02 kg-m/s

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The correct Answer is:
To find the linear momentum of a disc that is rotating about its axis, we need to understand the distinction between linear momentum and angular momentum. ### Step-by-Step Solution: 1. **Identify the Given Values:** - Mass of the disc (m) = 1 kg - Radius of the disc (r) = 10 cm = 0.1 m (convert cm to m) - Angular velocity (ω) = 2 rad/s 2. **Understanding Linear Momentum:** - Linear momentum (p) is defined as the product of mass and velocity (p = m × v). - For a rotating object, the linear velocity (v) of a point on the edge of the disc can be calculated using the formula: \[ v = \omega \times r \] 3. **Calculate the Linear Velocity:** - Substitute the values into the formula: \[ v = 2 \, \text{rad/s} \times 0.1 \, \text{m} = 0.2 \, \text{m/s} \] 4. **Calculate the Linear Momentum:** - Now, we can calculate the linear momentum using the mass and the linear velocity: \[ p = m \times v = 1 \, \text{kg} \times 0.2 \, \text{m/s} = 0.2 \, \text{kg m/s} \] 5. **Clarifying the Context:** - However, the question specifies that the disc is rotating about its axis without any translational motion. In such a case, the linear momentum of the entire disc as a rigid body is considered to be zero because it does not have a net translational movement in space. 6. **Final Answer:** - Therefore, the linear momentum of the disc is: \[ p = 0 \, \text{kg m/s} \] ### Summary: The linear momentum of the disc, given that it is only rotating and not translating, is **0 kg m/s**.

To find the linear momentum of a disc that is rotating about its axis, we need to understand the distinction between linear momentum and angular momentum. ### Step-by-Step Solution: 1. **Identify the Given Values:** - Mass of the disc (m) = 1 kg - Radius of the disc (r) = 10 cm = 0.1 m (convert cm to m) - Angular velocity (ω) = 2 rad/s ...
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