Coriolis Acceleration Calculation

The problem asks for the magnitude of the Coriolis acceleration experienced by a block sliding in a radial slot on a rotating disk.

Key Parameters

• Angular velocity of the disk: $\omega = 3$ rad/s
• Constant speed of the block relative to the slot: $v_{rel} = 0.2$ m/s

Coriolis Acceleration Formula

The Coriolis acceleration ($a_c$) in a rotating frame is given by the formula:

$ \vec{a}_c = 2 \vec{\omega} \times \vec{v}_{rel} $

Where:

• $\vec{\omega}$ is the angular velocity vector of the rotating frame (the disk).
• $\vec{v}_{rel}$ is the velocity vector of the object relative to the rotating frame (the block's velocity along the slot).

The angular velocity vector $\vec{\omega}$ is directed perpendicular to the disk's plane. The relative velocity $\vec{v}_{rel}$ is directed radially outwards (or inwards) along the slot. Since the radial direction is perpendicular to the angular velocity vector for a horizontal disk, the magnitude of the Coriolis acceleration is:

$ a_c = 2 \omega v_{rel} $

Magnitude Calculation

Substitute the given values into the formula:

$ a_c = 2 \times (3 \text{ rad/s}) \times (0.2 \text{ m/s}) $

$ a_c = 6 \times 0.2 \text{ m/s}^2 $

$ a_c = 1.2 \text{ m/s}^2 $

Conclusion

The magnitude of the Coriolis acceleration is 1.2 m/s$^2$. This corresponds to Option A.