Understanding Coriolis Acceleration Calculation

The question asks us to find the Coriolis component of acceleration for a block moving on a rotating link. This type of acceleration occurs when an object moves within a rotating reference frame.

Key Information Provided

• The block slides outward on the link at a uniform rate. This is the radial velocity ($v_r$).
• The radial velocity ($v_r$) = 30 m/s.
• The link is rotating at a constant angular velocity ($\omega$).
• The angular velocity ($\omega$) = 50 rad/s (counter clockwise).

Formula for Coriolis Acceleration

The Coriolis acceleration ($a_c$) is a fictitious acceleration observed in a rotating frame of reference. It is calculated using the following formula:

$$ a_c = 2 \omega v_r $$

Where:

• $a_c$ is the Coriolis acceleration.
• $\omega$ is the angular velocity of the rotating frame (the link in this case).
• $v_r$ is the velocity of the object (the block) relative to the rotating frame (along the radial direction).

Step-by-Step Calculation

Let's plug the given values into the formula:

1. Identify the angular velocity: $\omega = 50$ rad/s.
2. Identify the radial velocity: $v_r = 30$ m/s.
3. Substitute these values into the Coriolis acceleration formula:

   $$ a_c = 2 \times (50 \text{ rad/s}) \times (30 \text{ m/s}) $$

4. Perform the multiplication:

   $$ a_c = (100 \text{ rad/s}) \times (30 \text{ m/s}) $$

   $$ a_c = 3000 \text{ m/s}^2 $$

Result

The Coriolis component of acceleration for the block is 3000 m/s².