Question

A wheel of diameter 20 cm is rotating at 600 rpm. The linear velocity of a particle at its rim is:

• A. \( 6.28 \, \text{m/s} \)
• B. \( 12.56 \, \text{m/s} \)
• C. \( 18.84 \, \text{m/s} \)
• D. \( 3.14 \, \text{m/s} \)

Hint:

Always convert rpm to radians per second (\( \omega \)) when calculating linear velocity.

Answer 1

The Correct Option is A

The linear velocity \( v \) is given by: \[ v = r \cdot \omega, \] where \( r \) is the radius and \( \omega \) is the angular velocity. 

Given: \[ \text{Diameter} = 20 \, \text{cm} \Rightarrow r = \frac{20}{2} = 10 \, \text{cm} = 0.1 \, \text{m}. \] 

The angular velocity \( \omega \) is: \[ \omega = 2\pi f, \quad f = \frac{\text{rpm}}{60} = \frac{600}{60} = 10 \, \text{rps}. \] 

Substituting values: \[ v = 0.1 \cdot (2\pi \cdot 10) = 0.1 \cdot 20\pi \approx 6.28 \, \text{m/s}. \]