Glossary of Physics Formulas

Transcription

1 Glossary of Physics Formulas 1. Kinematic relations in 1-D at constant velocity Mechanics, velocity, position x - x o = v (t -t o ) or x - x o = v t x o is the position at time = t o (this is the beginning time and it can often be set to zero; hence the second equation shown). x is the position at time t v is the constant velocity 2. Kinematic relations x o is the position at t = 0 in 1-D at constant x - x o = v o t +½ a t 2 x is the position at time = t acceleration v o is the velocity at t = 0 (initial velocity) Mechanics, velocity, position, acceleration a is the constant acceleration 3. Distance covered during braking d =distance for braking to a complete stop. v o is the velocity before the brakes are applied. Mechanics, velocity, position, deceleration d = a is the absolute value of the deceleration. 4. (Ax, Ay) and (Bx, By) are the C=(Ax+Bx, Ay+By) Vector sum and components of the two vectors magnitude and A and B. velocities, momenta C = 5. Projectile range Mechanics, 2-D motion, gravity R= sin (2θ) v is the velocity of the projectile at the beginning (see figure below). g is the acceleration due to gravity (on Earth = 9.8m/s 2 ). θ is the angle (above the horizontal) at which the projectile is fired. 6. Speed of impact for a free-falling object free fall, accelerated motion, gravity v= v is the downward speed just before impact on the ground (in meters/seconds). g is the constant acceleration due to gravity = 9.8 m/s 2. h is the original height (in meters). Notice: Formula assumes that air resistance can be neglected.

2 7. Time of impact for a freefalling object t is the time of the impact on the ground (in seconds). g is the constant acceleration due to gravity = 9.8 m/s 2. h is the original height (in meters). free fall, accelerated motion, gravity t= Notice: Formula assumes that air resistance can be neglected. 8. p is the momentum of an object of mass m and velocity v. Momentum p= mv Notice: Momentum is a vector quantity, requiring magnitude AND direction. 9. J is the impulse delivered by an average force F that has Impulse been applied for a time equal to t. J = F t 10. Work Mechanics, energy, forces, newton s laws of motion, gravity, normal force, weight W = F d 11. Potential energy PE = mgh 12. Kinetic energy KE = ½ mv Total mechanical energy E tot = KE+PE= constant 14. Work-Energy theorem W= ΔKE W is the work done on an object (in Joules). F is the applied force (in Newtons). d is the distance (along F) the object moves (in meters). Notice: The amount of work depends also on the cosine of the angle between the direction of the force and the direction of motion. If this angle is zero, you get the work as indicated by the formula on the left. But if this angle is 90 then the work done is zero. PE is the potential energy due to the height of an object above the ground (in Joules). m is the mass. g is 9.8m/s 2 (near the surface of the Earth). h is the height above the ground. KE is the kinetic energy due to the motion of an object (in Joules). m is the mass. v is the speed of the object. One assumes that no energy losses occur such as heat (as a result of friction, for example). W is the work done on an object, in Joules (assuming no losses such as those produced by friction). Δ KE means change in the kinetic energy. Thus work sets things into motion.

3 15. Weight Mechanics, Newton s second law, gravity w= 16. Centripetal force circular motion, gravity, tension F c = w is the weight of an object (in Newtons). m is the mass of the object (in kilograms). g is the constant acceleration due to gravity = 9.8 m/s 2. Notice: Our weight is often associated with the pull of gravity. But more correctly it is the reaction (equal and opposite the pull of gravity) of the floor against our feet. F c is the force in Newtons, m is the mass in Kg, v is the speed (in meters/seconds) around the circle, R is the radius of the circle (in meters). Notice: The direction of the force is toward the center of the circle. 17. F is the NET force acting on an object of mass m. Newton s second law a is the acceleration that results from the action of the force. Mechanics, Newton s second law, gravity F= a= F/m 18. Static and kinetic friction Newton s laws of motion, gravity, normal force, weight F f = F f = Notice: This is one of the most important formulas in Physics. It tells us that whenever we observe an accelerated motion, there must be some unbalanced force acting on the object. It is important to realize that both acceleration and force are vector quantities. So there is acceleration (hence a force) even if an object changes direction, even if the speed is constant. F f is the force of friction (in Newtons). μ s and μ k are the coefficient for static and kinetic friction, numbers that depend only on the materials rubbing each other. They have no unit. F n is the normal force (in Newtons). Notice: The direction of the friction force is always opposite to the direction of motion.

4 19. Hooke s Law F = Newton s laws of motion, gravity, weight F is the force exerted by a spring. k is the spring constant (tells us how stiff the spring is). xo is the position of the free end of the spring (when no mass is attached to it). x is the position of the free end of the spring (when the mass is attached to it). Notice: The direction of the force is always opposite to the direction of the stretching, hence the minus sign in the formula. 20. Angular momentum Newton s laws of motion, gravity, rotational motion L = mvr 21. Torque Newton s laws of motion, rotational motion T = 22. Moment of Inertia Newton s laws of motion, rotational motion For a point mass m, rotating around a point at a distance R from the center I =mr 2 L is the angular momentum measured in Js. m is the mass of the rotating object. v is the rotational speed. R is the radius of rotation. Notice: In the absence of torques, angular momenta are conserved quantities. T is the torque, measured in unit of N m, and F is the force acting perpendicular to the radius R of rotation. Notice: The torque also depends on the sin of the angle of the force and the radius of rotation. So if this angle is zero, the torque is also zero, and it is maximum when the angle is 90. I is the equivalent of mass for rotational motion. It corresponds to rotational inertia, the same as mass corresponds to linear inertia. I is measured in kgm The unit of power is Watts = Joules/seconds. Power energy, work P =energy/time Or work/time A more powerful machine is one that does the same amount of work, but in a shorter amount of time. 24. Law of Universal Gravitation F is the force of attraction between two masses m and M whose centers are separated by the distance d. G is a universal constant equal to planetary motion, mass F = G 6.67 Nm 2 /kg 2 Notice: F is always attractive. This is Isaac Newton s greatest masterpiece.

5 25. Orbital and escape speed planetary motion, mass, circular motion v orb = v esc = v orb is the orbital speed of a satellite around a mass M at a distance d from the center of that mass. v esc is the escape speed of a satellite around a mass M at a distance d from the center of that mass. G is a universal constant (see 24). 26. T is the period of oscillation of the pendulum (full Period of a pendulum swing). T =2π L is the length of the pendulum. Mechanics, g is the acceleration due to gravity. 27. T C is the temperature in degrees Celsius. Temperature scales T F is the temperature in degrees Fahrenheit. T C = (T F - 32) thermometers, hot and cold T F = T C + 32 Notice: The value of 9/5 in the second equation is multiplied only by T C, hence there is no parenthesis. 28. Specific heat for homogeneous phases Q = mc ΔT 29. Q = ml f Latent heat of melting (fusion) and vaporization Q = ml v 30. Linear expansion of solids ΔL = L α ΔT 31. Volume expansion of a liquid ΔV = V β ΔT Q is the heat in Joules added or subtracted to a system (isolated) of mass m (in Kg). c is a specific heat constant (for water c= 4186 J/Kg C). ΔT is the change in temperature in degrees Celsius. Q is the heat in Joules added or subtracted to a system undergoing a phase change (at the melting and vaporization temperatures). m is the mass of the material (in Kg). L f (or L v ) are constants for that material. ΔL is the change in length (in meters) of an object due to the addition or removal of heat. L is the original length of the object. α is the coefficient of linear expansion, which depends on the material. ΔT is the change in temperature in degrees Celsius. ΔV is the change in volume (in m 3, liter, gallons, etc.) of a liquid due to the addition or removal of heat. V (in m 3, liter, gallons, etc.) is the original volume of the liquid. β is the coefficient of volume expansion, which depends on the material. ΔT is the change in temperature in degrees Celsius.

6 32. First law of thermo ΔE is the increase in internal energy of a system. ΔQ is the heat added to the system. ΔW is the work done by the system. ΔE = ΔQ ΔW 33. Ideal Gas Law pressure PV = nrt Special cases: (when T is constant) P 1 V 1 = P 2 V 2 (when V is constant) P 1 / T 1 = P 2 /T 2 (when P is constant) V 1 / T 1 = V 2 /T Density Fluid, thermo ρ = m/v 35. Pressure Fluid, thermo P = F/A P is the pressure of the gas (in Pascals). V is the volume of the gas (in m 3 ). n is the number of moles of gas (1 mole= 6.02x10 23 molecules or atoms). R is a constant = T is the gas temperature (in Kelvin). ρ is the density of a material (pronounced rho, in Kg/m 3 ). m is the mass of the material (in Kg). V is the volume of the material (in m 3 ). P is the pressure ( in N/m 2 =Pascals). F is the force (in N). A is the area (in m 2 ). 36. P depth is the pressure ( in N/m 2 =Pascals) at a depth y (in m). at a depth in Pressure a fluid P depth = P surface + ρ g y P surface is the pressure at the surface. ρ is the density of the fluid (in Kg/m 3 ). g is 9.8m/s 2. Fluid y is the depth below the surface. 37. F B is the buoyant force, in Newtons, felt by an object Archimedes Principle immersed in a fluid. (It is directed upwards.) (buoyant force) F B =m fluid g m fluid is the mass of the fluid that is displaced by the object g is 9.8m/s 2. Fluid 38. This equation applies to two sections, A and B, of a tube where Bernoulli s Equation a fluid is steadily flowing Fluid, fluid flow P A +½ρ(v A ) 2 +ρgh A = P B +½ρ(v B ) 2 +ρgh B P A and P B are the pressures at sections A and B. v A and v B are the speed of the flow at sections A and B. h A and h B are the heights at sections A and B. g is 9.8m/s 2 and ρ is the density of the fluid.

7 39. v is the speed of the wave (in m/s). Speed of a traveling wave f is the frequency of oscillation (in sec v = f λ = Hertz). λ is the wavelength (in m). Wave motion, sound, light 40. Coulomb s Law Electricity F = k F is the force of attraction or repulsion, in Newtons, between two charges Q 1 and Q 2. (The unit of charge is called a Coulomb.) k is a constant approximately equal to 9 x10 9. d is the distance (in m) between the charges. 41. Electric field E is the electric field AT A POINT, AT A DISTANCE d FROM A CHARGE Q. k is a constant approximately equal to 9 x10 9. Electricity E= k 42. Electric field direction Electricity E is always directed AWAY from positive charges and INTO negative ones. (see 40) 43. V is the electric potential (in Volts) at a distance d (in m) Electric potential away from a charge Q (in Coulombs). V = k k is a constant approximately equal to 9 x10 9. Electricity 44. Ohm s Law Electricity V=RI or I=V/R V is the voltage (in Volts) measured between two points in a circuit. I is the DC current flowing between those points (in Amperes or Amps). R is the resistance (in Ohms, symbol: Ω) between the two points.

8 45. Magnitude of the magnetic force on a moving charge Electricity and magnetism F= qvb sin φ F is the force felt by the charge (in N). v is the charge speed (in m/s). B is the strength of the magnetic field (in Teslas) in which the charge q (in Coulombs) finds itself to travel. φ is the angle between the vector v and the vector B. Notice: The direction of F is perpendicular to both v and B according to the so-called right hand rule. 46. Magnitude of the magnetic F is the force felt by the charge (in N). B is the strength of the magnetic field (in Teslas) in force on a segment of a wire the vicinity of the segment of wire L (in m) is located. carrying current F= BIL sin φ φ is the angle between the direction of I and the vector B. Electricity and magnetism 47. B is the magnetic field (in Teslas). Magnetic field near a straight B= I is the current (in Amps). wire carrying current μ o is a constant equal to 4π R is the distance (in m, from the wire) where the magnetic field is measured. Electricity and magnetism Notice: The direction of B is circular around the wire. 48. B is the magnetic field (in Teslas) at the Magnetic field at the center of a B= center of the loop. circular loop of wire carrying I is the current (in Amps). current μ o is a constant equal to 4π R is the RADIUS (in m) of the loop. Electricity and magnetism Notice: The direction of B is as shown in the figure.

9 49. Transformer Electricity and magnetism The index 1 refers to the primary and the index 2 refers to the secondary of the transformer. V is the voltage. I is the current. N is the number of turns. 50. Reflection at a mirror Wave propagation, acoustics, optics θ i is the incident angle made by a beam (of light or sound) relative to the normal line. θ R is the angle of reflection still relative to the normal line (see figure). θ i = θ R 51. Index of refraction n is the index of refraction of a transparent material. c is the speed of light as measured in vacuum n = (c= 3 m/s). Optics v is the speed of light inside that material (always less than c). 52. n i sin θ i = n r sin θ n r i and n r are the indexes of refraction of the Snell s Law incident and refracted materials. Optics θ i is the incident angle made by a beam relative to the normal line. θ r is the angle of refraction still relative to the normal line (see figure). 53. E is the energy of an individual photon (in Joules). Energy of a photon f is the frequency of that photon (in Hertz). E= h f h is Planck s constant whose value is Modern Physics

10 54. λ is the wavelength associated with an object (in m). Matter waves h is Planck s constant whose value is λ= h/mv. m is the mass of the object (in Kg). Modern Physics v is its speed (in m/s). Name 55. Percentage formula Formula % difference = Laboratory methods 100