Describe qualitatively the acceleration acting on a bead that, sliding along a frictionless wire, moves inward with constant speed along a flat spiral.

Question

Navjyot Kalra · Answer

The magnitude of the acceleration of the bead moving in a spiral path centered about a point say P and moving with constant speed v₀ is given as:

Here r is the magnitude of position vector of the bead relative to point P.
Using the relation above, one can deduce that if the bead slides into the spiral with constant speed, the magnitude of acceleration, which is

, increases. To account for this larger acceleration, larger centripetal force must act on the bead. Therefore the acceleration of the bead moving into the spiral will keep of increasing linearly with linear decrease in value of r.

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Describe qualitatively the acceleration acting on a bead that, sliding along a frictionless wire, moves inward with constant speed along a flat spiral.

Describe qualitatively the acceleration acting on a bead that, sliding along a frictionless wire, moves inward with constant speed along a flat spiral.

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