Is there a foce acting towards the circumferace also?

Question

When a stone is whirled around using a string there is a force acting towards the centre of the cirlcle. Is there a force acting towards the circumferance too?

Answer 1

No. There are some who will tell you that there is a centrifugal force but this force is an illusion. The net force acts to hold the rock in the circle. The velocity of the rock at any given instant is tangent to the circle. The force acts to overcome the inertia and to stop the rock from going in a straight line. Cut the string and the force is gone. The rock won't veer off like it would if there were some force acting in that direction. It would just fly off tangent to the circle.

Answer 2

If the rotaion is at a constant angular velocity, there is no tangential acceleration a = alpha*R; where alpha is the angular acceleration which is zero when the angluar velocity is fixed. That is, alpha = dw/dt = 0 because w = constant. If there is no tangential acceleration, there is no tangential force ALONG the circumference.

But there has to be a force outward along the string, FROM the circumerence of the swing. Why? Because that stone continues to stay on the end of the string. It is neither moving inward toward the center of rotation, nor outward away from the end of the string. In other words, there is no net force acting along the radius of rotation and on the stone.

The string is clearly pulling in on the stone; cut the string and bye bye stone. And that pull is called centripetal force P. For a satellite rotating a planet, centripetal force is the force of gravity coming from the planet. Centripetal force is real, it is caused by real, physical things. And, by definition, it is the force directed inward along the rotational radius towards the center of rotation.

So if there is no net radial force on the stone, what's counteracting or offsetting the real centripetal force? That would be a force directed outward from the stone on the circumference of the swing arc. So this force is not really directed towards the circumference, but it is directed outward from the circumference. And we call this outward one centrifugal force C.

Then, in math talk, f = P - C = 0; where f is the net force acting on that stone along the radius of rotation. P is acting towards the center and C is acting outward from the circumference where the stone is at the time. The string is pulling inward witha force P and .... Wait a minute, what's pulling or pushing outward on the stone? What's the source of the C force?

In truth, some folks will tell you it's a virtual or faux force with no real source other than being the equal, but opposite reaction to centripetal force. That may be true (although not everyone agrees). Here's what I think.

Newton's first law about inertia says a body in motion will travel in a straight path unless otherwise acted on by a force. For the swinging stone, that force is P, which keeps pulling the stone off its straight path to make it curve around in the swing arc. But the stone really does not want to curve, it wants to stay going in a straight line, along the tangent direction at any given moment in time. And it's inertia that causes this preference for a straight path.

So my hypothesis is that inertia is the source of centrifugal force C. There is a theory about something called the Higgs Field, a force field of Higgs Bosons. The theory suggests that inertial mass results when quanta are aligned against the direction of the Higgs Field in higher dimensions.

Centrifugal force is like friction force, but in higher dimensions. It is simply the force pulling outward against centripetal force when overcoming the "friction" of the Higgs Field and inertia is what we call that friction. [See source.]

To illustrate this hypothesis, assume P is the push on a block of wood sitting on a wooden plank. Let C = kN = kmg, the frcition force pushing back against the push. Like the Higgs Field force, this friction force also depends on the size of the mass. When f = P - C = 0, the block fails to move because the two forces are equal, but opposite forces.

In a similar way, when that stone on the end of a string fails to move along the radius of rotation, it's because of the inertial friction force (C) caused by the Higgs Field is pushing back on the centripetal force. The inertial friction force along the radius of rotation is what most people would call centrifugal force.

BTW: Most people solve for P by solving for C = mv^2/R (m is mass, v is tangential velocity, and R is the turn radius)because solving for centrifugal force is easier than solving for centripetal force. But that works because when that stone, for example, hangs onto the string, f = 0 = P - C; so that P = C = mv^2/R. C and P have the same magnitudes even though they have opposite directions.

Answer 3

If the stone has constant angular velocity, then there is no tangential force, but if it has angular acceleration, it will have tangential acceleration and hence tangential force, i.e., along the circumference.