Question

A metal rod of length $ L = 0.8 \, \text{m} $ is rotating about its center with an angular velocity $ \omega = 10 \, \text{rad/s} $. What is the linear velocity of a point on the rod at a distance $ r = 0.4 \, \text{m} $ from the center?

• A. \( 4 \, \text{m/s} \)
• B. \( 8 \, \text{m/s} \)
• C. \( 2 \, \text{m/s} \)
• D. \( 6 \, \text{m/s} \)

Hint:

Remember: Linear velocity is directly proportional to both the radius and the angular velocity.

Answer 1

The Correct Option is A

Step 1: Formula for linear velocity
The linear velocity \( v \) of a point on a rotating object is given by: \[ v = r \omega \] where: - \( r \) is the radius (distance from the center), - \( \omega \) is the angular velocity.
Step 2: Substitute the given values
Given: - Radius \( r = 0.4 \, \text{m} \) - Angular velocity \( \omega = 10 \, \text{rad/s} \) \[ v = 0.4 \times 10 = 4 \, \text{m/s} \]
Answer:
Therefore, the linear velocity of the point on the rod is \( 4 \, \text{m/s} \). So, the correct answer is option (1).