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 calculated using the formula: \[ v = r \cdot \omega, \] where \( r \) represents the radius and \( \omega \) denotes the angular velocity.

The diameter is provided as 20 cm, from which the radius \( r \) is derived: \[ \text{Diameter} = 20 \, \text{cm} \Rightarrow r = \frac{20}{2} = 10 \, \text{cm} = 0.1 \, \text{m}. \] 

The angular velocity \( \omega \) is determined by the frequency \( f \), where \( f \) is in revolutions per second (rps): \[ \omega = 2\pi f, \quad f = \frac{\text{rpm}}{60} = \frac{600}{60} = 10 \, \text{rps}. \] 

Upon substituting the values, the linear velocity \( v \) is found to be: \[ v = 0.1 \cdot (2\pi \cdot 10) = 0.1 \cdot 20\pi \approx 6.28 \, \text{m/s}. \]