# Force to keep photon in circular motion

• quietrain
In summary, the conversation discusses the calculation of the force needed to keep a proton moving in a circle with a 1.0 km radius, with an energy of 2.5 × 10−10 J. The attempt at finding the force involves determining the proton's speed and using the formula f = mv^2/R, however the resulting answer does not match the expected answer. The conversation then delves into the concept of relativistic mass and its relation to the speed of light. The second attempt to solve the problem involves using the equation E = hf and converting to T = 1/f, but this also yields a speed faster than the speed of light. The conversation concludes by questioning whether relativistic mass must be considered for any

## Homework Statement

A proton has an energy of 2.5 × 10−10 J. What force is needed to keep it going in
a circle having a 1.0 km radius

## The Attempt at a Solution

so i tried to find v first.

total energy E = 2.5 x 10-10 J =$$\gamma$$ mc2

so m = photon mass = 1.67 x 10-27

so i found $$\gamma$$ = 1.66
and v = 0.798c

so when i sub into f = mv2/R , i get f = 9.57 x 10-14

but the answer is 1.6 x 10-13

which means that the photon speed is roughly 0.9++ c

so anyone knows what's wrong?

btw why can't i use E= hf, get f, convert to T =1/f, then use circumference / T = v ?
i realize that v i get is faster than the speed of light. but which step is wrong in this attempt?

thanks!

hmm.. i realize that i have to use relativistic mass in this case. to get the answer.

so basically anything that has speed comparable to c, we have to use relativistic mass?

so gamma was 1.66, so it means that as the photon moves with speed close to light, its mass increases? 1.66m ? so is this correct? speed increase = mass increase? from E = mc ^2btw, anyone knows what's wrong with my 2nd type of attempt in the first post?

## 1. What is the force that keeps a photon in circular motion?

The force that keeps a photon in circular motion is known as the centripetal force. This force acts towards the center of the circular path and is responsible for keeping the photon moving in a circular motion.

## 2. How is the centripetal force calculated for a photon in circular motion?

The centripetal force for a photon in circular motion can be calculated using the formula F = mv^2/r, where m is the mass of the photon, v is its velocity, and r is the radius of the circular path.

## 3. Can the centripetal force acting on a photon be changed?

Yes, the centripetal force acting on a photon can be changed by altering its speed or the radius of its circular path. Increasing the speed of the photon or decreasing the radius will result in a stronger centripetal force.

## 4. What happens if there is no centripetal force acting on a photon in circular motion?

If there is no centripetal force acting on a photon in circular motion, the photon will continue to move in a straight line, tangent to the circular path. This is known as the law of inertia.

## 5. How does the mass of a photon affect the centripetal force in circular motion?

The mass of a photon does not affect the centripetal force in circular motion. This is because photons have no rest mass and therefore cannot be accelerated by a force. The centripetal force acts on the photon's energy and frequency, rather than its mass.