# Motion of Particles

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## Circular Motion

• Velocity = speed and direction of an object
• If an object is travelling in a circle then it is constantly changing direction.
• It is therefore accelerating so there must be a resultant force acting on it.*
• The force that keeps something moving in a circle is the centripetal force.

*Resultant force = the total force that results from two or more forces acting on a single object.

If the resultant force acting on a body is not zero, it will accelerate in the direction of the resultant force.

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## Cyclotrons

• In a cyclotron, a charged particle has a constant magnetic field applied to it.
• This is applied at right angles to the particle's motion (perpendicular) to provide the centripetal force needed for circular motion.
• A potential difference is placed across the gap between two electrodes (dees) to accelerate the particle across.
• The path of the particle spirals outwards as its speed increases. Eventually, it leaves the magnetic field and travels in a straight line towards another particle beam.
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## Uses of Particle Accelerators

• If a high energy proton is allowed to collide with a stable element, then the nucleus of that element will become an unstable nucleus of a different element.
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• The result is a radioactive isotope. The unstable isotope will emit α particles, β particles, γ rays or neutrons.
• Small cyclotrons can be used in hospitals to produce the short lived isotopes needed for PET scanners.
• Scientists can use particle accelerators to observe the radiation given off and to discover new types of particles. This helps scientists develop better explanations of the physical universe.
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## Momentum and Kinetic Energy

• Colliding objects have kinetic energy and momentum (mass x velocity).
• Momentum is always conserved. It is a vector so it has both size and direction.
• In an elastic collision, KE is also conserved.
• In an inelastic collision, KE is not conserved. It can be dissipated as other forms of energy such as heat or sound.
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## Annihilation

• When a positron meets an electron, the result is annihilation.
• They approach each other with the same mass but at opposite velocities.They therefore have equal but opposite momentum so the total momentum before collision is 0.
• Gamma rays are produced from annihilation. As momentum is always conserved, the two γ rays need to have a momentum of 0.
• The γ rays have the same energy (which has a mass equivalent) but opposite velocities. The momentum after collision is therefore 0.
• Charge is also conserved. An electron (-1) and a positron (+1) result in a neutral (0) charge. γ rays have no charge so therefore charge is conserved.
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## PET Scans

Positron emission tomography

• A radio isotope produced by a cyclotron emits positrons.
• The positrons are injected into the blood through a tracer. The tracer accumulates in various bodily tissues.
• After a short distance, the positrons will encounter an electron.
• Electron-positron annihilation will take place, emitting a pair of γ rays.
• The γ rays are detected by sensors positioned around the patient. Their detection allows a picture of the internal organs to be produced.
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