A bug sits on the edge of a rotating disk. Later, the bug begins to move toward the center of the disk. Does the bug exert a torque on the disk?
Sure, The angular momentum of the total bug/disk system has to remain constant since there is no external torque. The moment of inertia of the system decreases, so the angular velocity of the disc increases. There is therefore a tangential force exerted on the disk by the bug's feet :)
To determine whether the bug exerts a torque on the disk, we need to consider the factors involved in torque. Torque is the rotational equivalent of force. It depends on two main factors: the magnitude of the applied force and the distance of the force from the axis of rotation.
In this scenario, as the bug moves toward the center of the disk, it exerts a force on the disk. However, whether or not this force causes a torque depends on the distance of the force from the axis of rotation.
If the bug moves directly toward the center along a radial line, i.e., perpendicular to the radius from the center to the bug's starting position, then the force applied by the bug will act through the axis of rotation. In this case, the distance from the axis of rotation to the force is zero, resulting in no torque being exerted on the disk.
On the other hand, if the bug moves in an inward direction but not directly along a radial line, then the force applied by the bug will act at a distance from the axis of rotation. In this case, the magnitude of the torque depends on the magnitude of the force and the distance between the point of application and the axis of rotation.
Therefore, if the bug moves directly toward the center along a radial line, it does not exert a torque on the disk. However, if the bug moves inward but not directly along a radial line, it does exert a torque on the disk, which will cause rotational motion.