An insect of mass 'm' is traveling with velocity 'v' toward the circumference of a clockwise rotating disk (of angular velocity W) from its center, then the insect will experience... An insect of mass 'm' is traveling with velocity 'v' toward the circumference of a clockwise rotating disk (of angular velocity W) from its center, then the insect will experience a force of?
Understand the Problem
The question is asking about the force experienced by an insect with a certain mass and velocity as it travels towards the circumference of a rotating disk. It is related to the concepts of circular motion and the Coriolis effect.
Answer
The force experienced by the insect is $-2mWv$ along the right of it.
Answer for screen readers
The insect will experience a force of $-2mWv$ along the right of it.
Steps to Solve
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Understanding the Situation
The insect is moving toward the edge of a rotating disk. As the disk rotates, it creates a circular motion which affects the insect. -
Identifying Forces
As the insect moves, it experiences a Coriolis force due to its velocity and the angular velocity of the disk. The Coriolis force can be calculated using the formula:
$$ F_c = -2m(\vec{\omega} \times \vec{v}) $$
where $m$ is mass, $\vec{\omega}$ is the angular velocity, and $\vec{v}$ is the velocity of the insect. -
Direction of Forces
We determine the direction of the force by using the right-hand rule. For an insect moving toward the circumference of a clockwise rotating disk, the Coriolis force will act to the right of its direction of motion. -
Final Calculation of Force
Substituting the known variables and considering the insect is moving toward the center, we have:
- Angular velocity $W$ (in radians/sec)
- Velocity $v$ (in m/s)
Thus, the force becomes:
$$ F = -2mWv $$
and it acts to the right of the insect's trajectory.
The insect will experience a force of $-2mWv$ along the right of it.
More Information
This force arises due to the rotational reference frame of the disk, which causes a deflection in the insect's path. The Coriolis effect is significant in rotating systems, affecting the trajectory of objects moving within them.
Tips
- Misunderstanding the direction of the Coriolis force. Always apply the right-hand rule correctly.
- Neglecting the effect of angular velocity when calculating the forces.
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