Question

A slider sliding at 100 mm/s on a link which is rotating at 60 rpm is subjected to Coriolis acceleration of magnitude:

• A. \( 200 \pi \, \text{mm/s}^2 \)
• B. \( 200 \pi^2 \, \text{mm/s}^2 \)
• C. \( 400 \pi \, \text{mm/s}^2 \)
• D. \( 400 \pi^2 \, \text{mm/s}^2 \)

Hint:

Remember to always convert the angular velocity to radians per second before using it in the Coriolis acceleration formula. Ensure the units of linear velocity are consistent with the desired units of acceleration.

Answer 1

The Correct Option is C

Step 1: Recall the formula for Coriolis acceleration.
The Coriolis acceleration \( a_c \) is given by the formula: \[ a_c = 2 v \omega, \] where \( v \) is the velocity of the slider relative to the rotating link, and \( \omega \) is the angular velocity of the rotating link. Step 2: Convert the angular velocity from rpm to rad/s.
The angular velocity is given as 60 rpm (revolutions per minute). To convert it to rad/s (radians per second), we use the conversion factor \( \frac{2\pi \, \text{radians}}{1 \, \text{revolution}} \) and \( \frac{1 \, \text{minute}}{60 \, \text{seconds}} \): \[ \omega = 60 \, \frac{\text{rev}}{\text{min}} \times \frac{2\pi \, \text{rad}}{1 \, \text{rev}} \times \frac{1 \, \text{min}}{60 \, \text{s}} = 2\pi \, \text{rad/s}. \] Step 3: Identify the velocity of the slider.
The velocity of the slider relative to the rotating link is given as \( v = 100 \, \text{mm/s} \). Step 4: Substitute the values into the Coriolis acceleration formula.
\[ a_c = 2 v \omega = 2 \times (100 \, \text{mm/s}) \times (2\pi \, \text{rad/s}). \] Step 5: Calculate the magnitude of the Coriolis acceleration.
\[ a_c = 400 \pi \, \text{mm/s}^2. \] Step 6: Select the correct answer.
The magnitude of the Coriolis acceleration is \( 400 \pi \, \text{mm/s}^2 \), which corresponds to option 3.