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Grade 11 Physics: formula sheet

Kinematics, forces, energy, waves, electricity and heat · 43 formulas · metric edition 1

Download the PDF: 2 pagesThe full study guide: modules, problems, answer key
Module 1 · Kinematics
Physics 11-1 Speed, Distance & Time
v=dtv = \tfrac{d}{t}
Average speed from distance travelled and elapsed time.
Physics 11-2 Final Velocity (Uniform Acceleration)
v=v0+atv = v_0 + a t
Final velocity after accelerating uniformly from an initial velocity for a given time.
Physics 11-3 Displacement (Uniform Acceleration)
d=v0t+12at2d = v_0 t + \tfrac{1}{2} a t^2
Distance travelled under constant acceleration, starting from an initial velocity, over a time t.
Module 2 · Forces & Newton's laws
Physics 11-4 Newton's Second Law
F=maF = m a
Force equals mass times acceleration.
Physics 11-5 Weight (W = mg)
W=mgW = m g
Weight of a mass at Earth's surface, using standard gravity g = 9.80665 m/s² (exact by definition).
Physics 11-6 Kinetic Friction Force (f = μₖN)
fk=μkNf_k = \mu_k N
Friction force resisting a sliding surface, equal to the coefficient of kinetic friction times the…
Physics 11-7 Maximum Static Friction (f = μₛN)
fs,max⁡=μsNf_{s,\max} = \mu_s N
Largest static friction force available before an object breaks loose and slides, from the static…
Physics 11-8 Hooke's Law
F=kxF = k x
Restoring force of an ideal spring, proportional to its displacement from rest.
Physics 11-9 Rope Tension When Lifting a Mass
T=m(g+a)T = m\left(g + a\right)
Tension in a rope lifting a mass with an upward acceleration, exceeding the static weight by the…
Module 3 · Energy, work & power
Physics 11-10 Work (W = Fd cos θ)
W=Fdcos⁡θW = F d \cos\theta
Work done by a constant force acting at an angle to the displacement.
Physics 11-11 Kinetic Energy
Ek=12mv2E_k = \tfrac{1}{2} m v^{2}
Energy of a mass in motion.
Physics 11-12 Gravitational Potential Energy (U = mgh)
U=mghU = m g h
Energy stored by raising a mass to height h near Earth's surface, with g = 9.80665 m/s².
Physics 11-13 Work–Energy Theorem
W=12m(v2−v02)W = \tfrac{1}{2} m \left(v^{2} - v_0^{2}\right)
Net work done on an object equals its change in kinetic energy, linking force and distance to a…
Physics 11-14 Power (P = W/t)
P=WtP = \frac{W}{t}
Average power as work or energy delivered per unit time.
Physics 11-15 Power from Force and Velocity (P = Fv)
P=FvP = F v
Instantaneous power delivered by a force parallel to the velocity.
Physics 11-16 Machine Efficiency
η=WoutWin\eta = \frac{W_{out}}{W_{in}}
Efficiency of a machine as useful work out divided by work in, with the shortfall lost to friction,…
Module 4 · Waves & sound
Physics 11-17 Period-Frequency Relation
T=1fT = \frac{1}{f}
Period and frequency are reciprocals: seconds per cycle versus cycles per second.
Physics 11-18 Wave Speed (v = fλ)
v=fλv = f \lambda
The universal wave equation: a wave's speed equals its frequency times its wavelength.
Physics 11-19 Speed of Sound in Air
v=331.3+0.606 TCv = 331.3 + 0.606\, T_C
The speed of sound in dry air grows about 0.6 m/s for every degree Celsius above freezing.
Physics 11-20 Fundamental Frequency of a String
f=v2Lf = \frac{v}{2L}
Lowest standing-wave frequency of a string fixed at both ends.
Physics 11-21 Wave Speed on a String
v=Fμv = \sqrt{\frac{F}{\mu}}
Waves travel faster on a tighter, lighter string: speed is the square root of tension over linear…
Physics 11-22 Harmonic Frequencies
fn=nf1f_n = n f_1
The nth harmonic of a vibrating system is n times its fundamental frequency.
Physics 11-23 Fundamental of a Closed Pipe
f=v4Lf = \frac{v}{4L}
A pipe closed at one end resonates with a quarter wavelength inside, giving a fundamental of v/4L.
Physics 11-24 Decibel Sound Level
β=10log⁡10 ⁣(II0)\beta = 10 \log_{10}\!\left(\frac{I}{I_0}\right)
Sound level in decibels compares an intensity to the threshold of hearing, I₀ = 10⁻¹² W/m².
Physics 11-25 Sound Intensity (I = P/A)
I=PAI = \frac{P}{A}
Sound intensity is the acoustic power passing through each square metre of surface.
Physics 11-26 Inverse-Square Law for Sound
I=P4πr2I = \frac{P}{4\pi r^{2}}
A point source's intensity falls with the square of distance as its power spreads over an expanding…
Physics 11-27 Doppler Effect (Approaching Source)
f′=fvv−vsf' = \frac{f v}{v - v_s}
Observed frequency rises when a sound source approaches, as each wavefront is emitted closer to the…
Physics 11-28 Doppler Effect (Approaching Observer)
f′=f(v+vo)vf' = \frac{f (v + v_o)}{v}
A listener moving toward a stationary source meets wavefronts more often and hears a higher…
Physics 11-29 Beat Frequency
fbeat=f1−f2f_{\text{beat}} = f_1 - f_2
Two nearby tones interfere to produce a loudness pulse at their difference frequency, with f₁ the…
Module 5 · Electricity & magnetism
Physics 11-30 Electric Charge (Q = It)
Q=ItQ = I t
Total charge transferred by a steady current flowing for a given time.
Physics 11-31 Ohm's Law
V=IRV = I R
Relates the voltage across a conductor to the current through it and its resistance.
Physics 11-32 Two Resistors in Series
Rt=R1+R2R_{t} = R_{1} + R_{2}
Total resistance of two resistors connected end to end is simply their sum.
Physics 11-33 Two Resistors in Parallel
Rt=R1R2R1+R2R_{t} = \frac{R_{1} R_{2}}{R_{1} + R_{2}}
Total resistance of two resistors connected side by side: product over sum, always less than either…
Physics 11-34 Electrical Power (P = VI)
P=VIP = V I
Power delivered to a component as the product of the voltage across it and the current through it.
Physics 11-35 Electrical Power (P = I²R)
P=I2RP = I^{2} R
Power dissipated as heat in a resistance carrying a current (Joule heating).
Physics 11-36 Electrical Power (P = V²/R)
P=V2RP = \frac{V^{2}}{R}
Power dissipated in a resistance held at a fixed voltage.
Physics 11-37 Electrical Energy (E = Pt)
E=PtE = P t
Energy consumed by a device drawing constant power over a period of time.
Physics 11-38 Magnetic Force on a Current-Carrying Wire
F=BILsin⁡θF = B I L \sin\theta
Magnitude of the force on a straight current-carrying wire in a uniform magnetic field.
Physics 11-39 Transformer Voltage Ratio
VsVp=NsNp\frac{V_{s}}{V_{p}} = \frac{N_{s}}{N_{p}}
Relates the primary and secondary voltages of an ideal transformer to its turns ratio.
Module 6 · Heat
Physics 11-40 Sensible Heat (Q = mcΔT)
Q=mcΔTQ = m c \Delta T
Heat needed to change a mass's temperature: mass times specific heat times the temperature change.
Physics 11-41 Latent Heat
Q=mLQ = m L
Heat absorbed or released when a mass changes phase at constant temperature.
Physics 11-42 Heat Conduction Rate
P=kAΔTdP = \tfrac{k A \Delta T}{d}
Steady-state heat flow through a slab by Fourier's law of conduction.
Physics 11-43 Thermal Linear Expansion
ΔL=αL0ΔT\Delta L = \alpha L_0 \Delta T
Length change of a solid caused by a temperature change, via the linear expansion coefficient.