Question

circular motion

Answer 1

How can the speed of an object undergoing vertical circular motion be constant?

Answer 2

Unless there is some kind of external force being applied (apart from gravity) the speed should vary due to the conservation of energy. E goes from being 1/2mv^2 at the bottom to being mgh + 1/2mv^2.
So yes, if g=0 then v could be constant. Alternatively, if some force is applied to accelerate the particle when dh/dt > 0 this could make up for the Ekin lost to Epot. Though you would then have to reabsorb this energy when dh/dt < 0

Answer 3

The magnitude of velocity is constant, i.e. speed is constant..
However, there is a 'centripetal force' acting towards the center which is responsible for just changing the direction of velocity. (The force is perpendicular to the direction of motion. so it can only bring a change only in direction not in magnitude of velocity) And since the direction of velocity is changing constantly, there is acceleration and the acceleration is radial.. (Remember the force is towards the center).
Through all these, the magnitude of velocity never changes. so, the speed is constant!

Answer 4

So if there is no external force, speed HAS to change right??

Answer 5

If there is no external force, speed would NEVER change. Though in a real life situation we have air resistance and gravity, so speed does inevitably change. The issue is that the external forces are inconsistent, thus resulting in an inconsistent Ekin also.