Question

A slider sliding at 15 m/s on a link which is rotating at 30 r.p.m, is subjected to Coriolis acceleration of magnitude

• A. \( \frac{3\pi}{\text{m/s}^2} \)
• B. 30 m/s\(^2\)
• C. \( \frac{4\pi}{\text{m/s}^2} \)
• D. 40 m/s\(^2\)

Hint:

The Coriolis acceleration depends on the velocity of the slider and the angular velocity of the rotating system.

Answer 1

The Correct Option is A

Step 1: Define the Coriolis acceleration formula.
The Coriolis acceleration is calculated using the following equation:\[a_C = 2v \omega\]Where \( v \) represents the slider's velocity and \( \omega \) represents the rotating link's angular velocity.Step 2: Convert the provided values.
We have \( v = 15 \, \text{m/s} \) and \( \omega = 30 \, \text{r.p.m.} \). Converting r.p.m. to radians per second, we get \( \omega = \frac{30 \times 2\pi}{60} \, \text{radians per second} = \pi \, \text{rad/s} \).Step 3: Compute the Coriolis acceleration.
Substituting the values into the formula \( a_C = 2 \times 15 \times \pi = 30\pi \, \text{m/s}^2 \), we find the Coriolis acceleration to be \( \frac{3\pi}{\text{m/s}^2} \). Final Answer: \[ \boxed{\frac{3\pi}{\text{m/s}^2}} \]