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123 Terms
What is a radian?
The angle subtended at the centre of a circle by an arc equal in length to the radius.
What is angular speed (ω)?
The change in angular displacement per unit time.
What is centripetal acceleration?
An acceleration of constant magnitude always directed towards the centre of the circle.
What causes centripetal acceleration?
A force of constant magnitude always perpendicular to the direction of motion (centripetal force).
What is a gravitational field
A region around an object with mass in which another object with mass experiences a force.
Define gravitational field strength
The gravitational force per unit mass at a point.
Why is g approximately constant near Earth's surface?
Because the change in height is negligible compared to Earth's radius, so r barely changes and g = GM/r² stays nearly constant.
What is a geostationary orbit?
A satellite orbiting directly above the equator, west to east, with a period of 24 hours, so it remains above the same point on Earth's surface. Used for communication satellites.
Define gravitational potential at a point.
The work done per unit mass in bringing a small test mass from infinity to that point. Units: J kg⁻¹. φ = -GM/r
Why is gravitational potential always negative?
Zero potential is defined at infinity. As a mass approaches another, it loses energy, and work is done by the two masses to bring them closer together so potential is less than zero.
What is gravitational potential energy of two point masses?
Ep = -GMm/r
What is thermal equilibrium?
When two objects in thermal contact have no net energy flow between them — they are at the same temperature.
In which direction does thermal energy flow?
From a region of higher temperature to a region of lower temperature.
What physical properties can be used to measure temperature?
Expansion of a liquid, volume of a gas at constant pressure, resistance of a metal, e.m.f. of a thermocouple, resistance of a semiconductor (thermistor).
What makes the thermodynamic temperature scale special?
It does not depend on the property of any particular substance. It is independent of any material.
What is absolute zero?
The lowest possible temperature, 0 K (= -273.15°C), at which all substances have minimum internal energy and an ideal gas has zero pressure and zero energy.
Convert between Kelvin and Celsius.
T/K = θ/°C + 273.15
Define specific latent heat of fusion.
The energy required to change unit mass of solid to liquid without change in temperature. Lf = ΔQ/Δm. Units: J kg⁻¹
Define specific latent heat of vaporisation.
The energy required to change unit mass of liquid to vapour without change in temperature. Lv = ΔQ/Δm. Units: J kg⁻¹
What is the Avogadro constant?
NA = 6.02 × 10²³. The number of particles in one mole of any substance.
What is an ideal gas?
A gas that obeys pV = nRT at all temperatures, pressures and volumes.
State the equation of state for an ideal gas in two forms.
pV = nRT (n = number of moles, R = 8.31 J K⁻¹) and pV = NkT (N = number of molecules, k = Boltzmann constant)
What is the Boltzmann constant and how is it related to R?
k = R/NA = 1.38 × 10⁻²³ J K⁻¹
State the basic assumptions of kinetic theory.
No intermolecular forces except during collisions → potential energy is zero, all internal energy is kinetic. 2. Volume of molecules negligible compared to container → gas is mostly empty space. 3. Collisions are perfectly elastic → kinetic energy is conserved. 4. Molecules move in random directions with random speeds → pressure is equal in all directions. 5. Time of collision negligible compared to time between collisions → forces only act during brief impacts.
What is internal energy?
The sum of a random distribution of kinetic and potential energies associated with the molecules of a system.
What determines the state of a system and what determines its temperature?
Potential energy determines the state; kinetic energy determines the temperature.
State the first law of thermodynamics.
ΔU = q + W, where ΔU = increase in internal energy, q = energy supplied by heating, W = work done on the system.
What is the work done when a gas expands at constant pressure?
W = pΔV. If the gas expands, it does work on surroundings so ΔU = q - pΔV.
What are the conditions for simple harmonic motion?
The magnitude of acceleration is proportional to displacement from a fixed point, and acceleration is always directed opposite to the displacement (towards the fixed point). a = -ω²x
State the equations for displacement, velocity and acceleration in SHM.
x = x₀sinωt, v = x₀ωcosωt = ±ω√(x₀² - x²), a = -x₀ω²sinωt. Maximum speed: v₀ = ωx₀
Describe the energy changes in SHM.
Energy continuously transfers between kinetic and potential energy. Total energy is constant. Ek = ½mω²(x₀² - x²), Ep = ½mω²x², Total E = ½mω²x₀²
What is damping?
When a resistive force acts on an oscillating system, causing the amplitude to gradually decrease. The period stays constant.
Distinguish between light, critical and heavy damping.
Light: oscillation gradually fades away. Critical: displacement returns to zero in the minimum time without oscillating. Heavy: displacement slowly returns to zero without oscillating, taking longer than critical.
What is resonance?
When a system is forced to oscillate at its natural frequency, the amplitude reaches a maximum. All forced oscillations vibrate at the driving frequency, not their own natural frequency.
What is natural frequency?
The frequency at which an object vibrates when allowed to do so freely, without any driving force.
How do you draw electric field lines?
Lines go away from positive charges, towards negative charges. Closer lines = stronger field. Lines never cross or touch.
What is the electric field strength in a uniform field?
E = ΔV/Δd, where ΔV is the potential difference and Δd is the plate separation.
What path does a charged particle follow in a uniform electric field perpendicular to its motion?
A parabolic path — constant velocity component perpendicular to field, constant acceleration parallel to field.
How does a capacitor discharge through a resistor?
Exponentially. Q = Q₀e^(-t/RC), V = V₀e^(-t/RC), I = I₀e^(-t/RC)
What is the time constant of a capacitor discharge circuit?
τ = RC. The larger R or C, the longer the capacitor takes to discharge.
State Fleming's left-hand rule.
First finger = Field, second finger = Current, thumb = Thrust (force). The force is at right angles to both the field and the current.
What is the force on a current-carrying conductor in a magnetic field?
F = BILsinθ, where θ is the angle between the conductor and the field. Zero force when parallel, maximum when perpendicular.
What is the force on a moving charge in a magnetic field?
F = Bqvsinθ. Direction found using Fleming's left-hand rule (conventional current direction for positive charges, opposite for negative).
What happens to a charged particle moving perpendicular to a magnetic field?
It travels in a circular path, with the magnetic force providing the centripetal force. Bqv = mv²/r, so q/m = v/Br.
What is the Hall effect?
When a current-carrying conductor is placed in a magnetic field, charge carriers are pushed sideways, creating a voltage (Hall voltage) across the width of the conductor. VH = BI/(ntq)
Why is a Hall probe made from a semiconductor rather than a metal?
Semiconductors have far fewer charge carriers (lower n), so drift velocity is much higher for the same current, producing a larger, more measurable Hall voltage.
What is a velocity selector?
Crossed electric and magnetic fields where only particles with speed v = E/B pass straight through undeflected, because the electric and magnetic forces exactly balance.
What is the r.m.s. value of current or voltage?
The value of direct current (or voltage) that would produce thermal energy at the same rate in a resistor. Ir.m.s. = I₀/√2, Vr.m.s. = V₀/√2
What is half-wave rectification?
Using a single diode to allow current in only one direction — the negative half of the AC cycle is blocked, giving a pulsed DC output.
What does a capacitor do in a rectification circuit?
It smooths the output by charging up during peaks and discharging between peaks, reducing the voltage ripple. Larger C or larger R gives smoother output.
What is the capacitance of an isolated conducting sphere?
C = 4πε₀r, where r is the radius of the sphere.
What is the magnetic field shape around a long straight current-carrying conductor?
Concentric circles centred on the wire. Direction found using the screw rule — clockwise for current going into the page, anticlockwise for current coming out.
What is the magnetic field shape of a flat circular coil?
Field lines pass through the centre of the coil, looping around the outside. Similar to a short bar magnet viewed end-on.
What is the magnetic field shape of a solenoid?
Similar to a bar magnet — uniform field inside, radial field outside. The end where current is anticlockwise is the N pole; clockwise is the S pole.
What is the difference between gravitational electric and magnetic fields for a stationary charge?
A stationary charge experiences a force in an electric field, no force in a magnetic field, and no force in a gravitational field (unless it has mass).
What is the difference between gravitational electric and magnetic fields for a moving charge?
A moving charge experiences forces in all three if it has mass and charge. The magnetic force is always at right angles to both the velocity and the field, unlike gravitational and electric forces which are parallel to the field.
What is the photon?
A quantum of electromagnetic energy. E = hf, where h is Planck's constant.
What is the photoelectric effect?
When electromagnetic radiation of sufficient frequency illuminates a metal surface, electrons (photoelectrons) are emitted.
What is the threshold frequency?
The minimum frequency of electromagnetic radiation needed to emit photoelectrons from a metal surface. Below this frequency, no electrons are emitted regardless of intensity.
State the photoelectric equation.
hf = Φ + ½mv²max, where Φ is the work function (minimum energy needed to release an electron) and ½mv²max is the maximum kinetic energy of the emitted electron.
Why is maximum kinetic energy of photoelectrons independent of intensity?
Because each electron interacts with a single photon. Intensity increases the number of photons, not the energy of each one. Only frequency determines the energy of individual photons.
