Physics Formulae

A Level H2 Physics (9479) Formulae Formulae highlighted in yellow is given in the formula list. Topic 1: Measurements Absolute Uncertainty 𝑥 ± ∆𝑥 Δx is the absolute uncertainty of x. Δx to 1 s.f. x to same d.p. as Δx Fractional Uncertainty ∆𝑥 𝑥 Δx is the absolute uncertainty of x. Fractional and percentage uncertainty to 2 s.f. Percentage uncertainty ∆𝑥 𝑥 × 100% First Principles ∆𝑧 ≈ 1 2 (𝑧𝑚𝑎𝑥 − 𝑧𝑚𝑖𝑛) Δz is the uncertainty of quantity z. zmax is the maximum value of z. zmin is the minimum value of z. Topic 2: Kinematics Velocity 𝑣 = 𝑑𝑠 𝑑𝑡 v is the velocity (m s-1) s is the displacement (m) t is the time (s) Average velocity 𝑣𝑎𝑣 = ∆𝑠 𝑡𝑡𝑜𝑡𝑎𝑙 Acceleration 𝑎 = 𝑑𝑣 𝑑𝑡 v is the velocity (m s-1) a is the acceleration (m s-2) t is the time (s) Average acceleration 𝑎𝑎𝑣 = ∆𝑣 𝑡𝑡𝑜𝑡𝑎𝑙 Equations of motion 𝑣 = 𝑢 + 𝑎𝑡 s is the displacement (m) u is the initial velocity (m s-1) v is the final velocity (m s-1) a is the acceleration (m s-2) t is the time (s) 𝑣2 = 𝑢2 + 2𝑎𝑠 𝑠 = 1 2 (𝑢 + 𝑣)𝑡 𝑠 = 𝑢𝑡 + 1 2 𝑎𝑡2 Topic 3: Dynamics Linear Momentum 𝑝 = 𝑚𝑣 p is the linear momentum (kg m s-1) m is the mass of the object (kg) v is the velocity of the object (m s-1) Newton’s 2nd Law 𝐹𝑛𝑒𝑡 = 𝑑𝑝 𝑑𝑡 = 𝑚𝑎 Fnet is the resultant force (N) p is the linear momentum (kg m s-1) t is the time taken for the object to change momentum (s) m is the mass of the object (kg) a is the acceleration of the object (m s-2) Newton’s 2nd Law involving Flowing Mass 𝐹𝑛𝑒𝑡 = 𝑚 𝑡 ∆𝑣 Fnet is the resultant force (N) m is the mass of the object (kg) t is the time taken for the amount of mass to flow out (s) v is the velocity (m s-1) Impulse ∆𝑝 = ∫ 𝐹 𝑑𝑡 Fnet is the resultant force (N) p is the linear momentum (kg m s-1) t is the time taken for the object to change momentum (s)

Principle of Conservation of Linear Momentum 𝑚1𝑢1 + 𝑚2𝑢2 = 𝑚1𝑣1 + 𝑚2𝑣2 m1 and m2 are the masses of the 2 colliding objects u1 and u2 are the velocities of the objects before collision v1 and v2 are the velocities of the objects after collision Principle of Conservation of Kinetic Energy 1 2 𝑚1𝑢12 + 1 2 𝑚2𝑢22 = 1 2 𝑚1𝑣12 + 1 2 𝑚2𝑣22 m1 and m2 are the masses of the 2 colliding objects u1 and u2 are the velocities of the objects before collision v1 and v2 are the velocities of the objects after collision Speed of approach vs speed of separation 𝑢1 − 𝑢2 = 𝑣2 − 𝑣1 u1 and u2 are the velocities of the objects before collision v1 and v2 are the velocities of the objects after collision Topic 4: Forces Hooke’s Law 𝐹 = 𝑘𝑥 F is the force applied (N) k is the elastic spring constant (N m-1) x is the change in length (m) Pressure 𝑝 = 𝐹 𝐴 p is the pressure (N m-2) F is the force (N) A is the area (m2) 𝑝 = ℎ𝜌𝑔 p is the pressure (N m-2) h is the height of the liquid (m) ρ is the density of the liquid (kg m-3) g is the acceleration due to gravity (N kg-1) Upthrust 𝑈 = 𝜌𝑉𝑔 = 𝑚𝑔 U is the upthrust exerted by fluid on an object (N) ρ is the density of the fluid (kg m-3) V is the volume of the fluid (m3) g is the acceleration due to gravity (N kg-1) m is the mass of the fluid (kg) 𝑈 = 𝐹𝑏𝑜𝑡𝑡𝑜𝑚 − 𝐹𝑡𝑜𝑝 U is the upthrust exerted by fluid on an object (N) F is the force by fluid on object (N) Moment of a Force 𝑀 = 𝐹𝑠 M is the moment of a force (Nm) F is the force causing a moment (N) s is the perpendicular distance to the pivot (m) Torque of a couple 𝑇 = 𝐹𝑑⊥ T is the torque (Nm) F are the forces in a couple. d is the perpendicular distance between the forces. Topic 5: Work, Energy and Power Work done 𝑊 = 𝐹𝑠 cos 𝜃 W is the work done (J) F is the force (N) s is the displacement in the direction of the force (m) θ is the angle between the 2 forces (°) Work done by a varying force 𝑊 = ∫ 𝐹 𝑑𝑠 W is the work done (J) F is the force (N) s is the displacement in the direction of the force (m) Work done by an expanding gas 𝑊 = 𝑝∆𝑉 W is the work done to push out the gas (J) p is the external pressure (N m-2) V is the difference in volume (m3) Translational kinetic energy 𝐸𝑘 = 1 2 𝑚𝑣2 Ek is the kinetic energy of the body (J) m is the mass of the body (kg) v is the translational velocity of the body (m s-2)

Gravitational potential energy near the Earth’s surface ∆𝐸𝐺𝑃 = 𝑚𝑔∆ℎ EGP is the gravitational potential energy change in a body (J) m is the mass of the body (kg) g is the acceleration due to gravity (m s-2) h is the change in the height of a body Elastic potential energy 𝐸𝐸𝑃 = 1 2 𝑘𝑥2 EEP is the elastic potential energy (J) k is the elastic spring constant (N m-1) x is the change in length (m) Power 𝑃 = 𝑊 𝑡 P is the power of the force (W) W is the work done by the force (J) t is the time taken (t) Instantaneous power 𝑃 = 𝒇 ⋅ 𝒗 = |𝒇||𝒗| cos 𝜃 P is the power of the force (W) f is the force (N) v is the velocity of the body (m s-1) Efficiency 𝐸𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 = 𝑢𝑠𝑒𝑓𝑢𝑙 𝑤𝑜𝑟𝑘 𝑑𝑜𝑛𝑒 𝑒𝑛𝑒𝑟𝑔𝑦 𝑖𝑛𝑝𝑢𝑡 × 100% = 𝑢𝑠𝑒𝑓𝑢𝑙 𝑝𝑜𝑤𝑒𝑟 𝑜𝑢𝑡𝑝𝑢𝑡 𝑝𝑜𝑤𝑒𝑟 𝑖𝑛𝑝𝑢𝑡 × 100% Topic 6: Circular Motion Angular Displacement 𝜃 = 𝑠 𝑟 θ is the angular displacement (rad) s is the arc length (m) r is the radius (m) Angular velocity 𝜔 = 𝑑𝜃 𝑑𝑡 ω is the angular velocity (rad s-1) θ is the angular displacement (rad) t is the time taken for the angular displacement to be swept out. Uniform circular motion 𝜔 = 2𝜋 𝑇 = 2𝜋𝑓 ω is the angular velocity (rad s-1) T is the period (s) f is the frequency (Hz) Relationship between angular and linear velocity 𝑣 = 𝑟𝜔 v is the linear or tangential velocity (m s-1) r is the radius of the circular path (m) ω is the angular velocity (rad s-1) Centripetal acceleration 𝑎𝑐 = 𝑣2 𝑟 = 𝑟𝜔2 ac is the centripetal acceleration (m s-2) v is the linear or tangential velocity (m s-1) r is the radius of the circular path (m) ω is the angular velocity (rad s-1) Centripetal force 𝐹𝑐 = 𝑚𝑣2 𝑟 = 𝑚𝑟𝜔2 Fc is the centripetal force (N) v is the linear or tangential velocity (m s-1) r is the radius of the circular path (m) ω is the angular velocity (rad s-1) Vertical motion (swung by a string) In general 𝑇 = 𝑚𝑣2 𝑟 + 𝑚𝑔 cos 𝜃 T is the tension in the string (N) m is the mass of the object (kg) v is the velocity of the object (m s-1) g is the acceleration due to gravity (m s-2) r is the radius of the circular path (m) θ is the angular displacement from bottom (rad) At the bottom 𝑇 = 𝑚𝑣2 𝑟 + 𝑚𝑔 At the top 𝑇 = 𝑚𝑣2 𝑟 − 𝑚𝑔 Topic 7: Gravitational Field Newton’s Law of Gravitation 𝐹 = 𝐺𝑚1𝑚2 𝑟2 F is the gravitational force (N) G is the gravitational constant (N m2 kg-2) m1 and m2 are the respective masses (kg) r is the distance between the masses (m)

Gravitational Field Strength 𝑔 = 𝐺𝑀 𝑟2 g is the gravitational field strength (m s-2 or N kg-1) G is the gravitational constant (N m2 kg-2) M is the mass of the object providing the gravitational field. (kg) r is the distance between the centre of mass of the mass providing the gravitational field and the point. (m) 𝑔 = − 𝑑𝜙 𝑑𝑟 ϕ is the gravitational potential (J kg-1) g is the gravitational field strength (m s-2 or N kg-1) r is the distance between the centre of mass of the mass providing the gravitational field and the point. (m) Gravitational potential 𝜙 = − 𝐺𝑀 𝑟 ϕ is the gravitational potential (J kg-1) G is the gravitational constant (N m2 kg-2) M is the mass of the object providing the gravitational field. (kg) r is the distance between the centre of mass of the mass providing the gravitational field and the point. (m) Gravitational potential energy from a large distance 𝐸𝐺𝑃 = 𝑚𝜙 = − 𝐺𝑀𝑚 𝑟 ϕ is the gravitational potential (J kg-1) G is the gravitational constant (N m2 kg-2) M is the mass of the object providing the gravitational field. (kg) m is the mass that is placed inside the gravitational field. r is the distance between the centre of mass of the mass providing the gravitational field and the point. (m) Escape velocity 𝑣𝑒𝑠𝑐 = √2𝐺𝑀 𝑅 Vesc is the velocity needed to escape the influence of the gravitational field.