Mechanics
Velocity and speed
What is the difference between velocity and speed? Velocity is the vector equivalent of speed. Since speed is the distance travelled per unit time, this means that velocity is displacement travelled per unit time. If you're estimating how long…
Mechanics
Linear acceleration
…cceleration is m s-2. All of the equations of motion require constant acceleration. If the acceleration is constant, average velocity equals the average of the initial and final values. This leads to a suvat equation: \(s ={(u + v) \over 2}t\) Spee…
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Angular momentum and rotational kinetic energy
…angular velocity: \(L=I\omega\) \(L\) is angular momentum (kgm2s-1) \(I\) is moment of inertia (kgm2) \(\omega\) is angular velocity (rads-1) Angular momentum is a conserved quantity: total angular momentum remains constant. Ice skaters make good us…
Mechanics
Inertia, momentum and impulse
While Physics problems usually explore the interactions between force and motion with a focus on velocity and acceleration, we mustn't forget that mass has an equally significant part to play. Key Concepts Inertia Heavy bodies require a larger f…
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Age of the universe
We can calculate an estimate for the age of the universe based on the velocity at which galaxies are receding from our observations. Key Concepts The cosmic scale factor is defined as the size of the universe at a given time relative to its size now.…
Daily IA
This is Dharsh, he is doing his IA on the hump-back bridge measuring the velocity at which a ball takes flight when rolling over a circular bridges of different radii. To be able to determine lift off he split the plastic pipe allowing the ball to ta…
Mechanics
Collisions
Using the laws of conservation of energy it is possible to calculate the combined velocity of two astronauts colliding in space... ...in case that was on your bucket list :) You don't need to memorise everything on this page (you will always have…
Oscillations and waves
Graphical representation of waves
Wave motion can be represented by graphs. The axes can include x-displacement, y-displacement, velocity, acceleration and time. However, take care to realise that a graph is not a picture of a wave. Since there is no energy transfer, a pendulum wave…
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AHL Fluid dynamics
…rization of fluid flow. Key Concepts Streamlines Flowlines show the movement of particles in a fluid. Streamlines follow the velocity vectors of particles in a fluid. As with all vectors, streamlines will never intersect as they show the resultant ve…
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Equilibrium and angular acceleration
…is in equilibrium. A body travelling at constant speed is in translational equilibrium. A body rotating at constant angular velocity is in rotational equilibrium. Key Concepts A body is in rotational equilibrium if the sum of the anticlockwise torqu…
Mechanics
Kinematics
…t an object moving through a complete circle has a distance equal to the circumference but a displacement of zero! Speed and velocity have the same units, m s-1 , but speed is a scalar and velocity is a vector. Average speed is definied as the total…
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AHL Further cosmology
…entripetal force is equal to the gravitational force, \({m_\text{star}v^2\over r}={4\over 3}\pi G \rho rm_\text{star}\) The velocity of the star is proportional to the distance from the centre, \(v^2\propto r^2\Rightarrow v\propto r\) The equation t…
Oscillations and waves
Simple harmonic motion
…itude): \(x=x_0\cos{\omega t} \Rightarrow v=-\omega x_0\sin \omega t \) \(x_0\) is amplitude (m) \(t\) is time (s) \(v\) is velocity (ms-1) This velocity is derived by differentiating the displacement equation. Velocity can be found at any time by f…
Oscillations and waves
Doppler effect
…ncy is changed. However, the speed of the source relative to an observer within the source itself is constant. Calculating velocity We can use determined values of the frequency of the sound emitted by a source car in the video above as it approach…
IA 2022
…relationship between centripetal force and angular velocity? Theo: The relationship between the angle of projectile (θ) and velocity of the ball (v) in order to hit the target. Nejra: What is the relationship between the resistance and length of a w…
Mechanics
…What are the types of motion graphs? Motion graphs come in two main formats: displacement vs time (gradient is velocity) and velocity vs time (gradient is acceleration and area is displacement). Find out more. How do you use the equations of motion?…
Mechanics
Projectile motion
…time. This means that the body is modelled as a particle. We can think of projectile motion as two problems in one: constant velocity horizontally and constant acceleration vertically. The motions in both directions have one common feature... time! V…
Circular motion and gravity
Circular motion
…ced circular motion. Here are some common thoughts among students... If your speed is constant how can you be accelerating? Velocity is a vector quantity. Anything travelling in a circular path is changing direction and, therefore, accelerating. A r…
Oscillations and waves
Equations for SHM
…soidally related to time. This means that the displacement equation with respect to time will contain either sin or cos. The velocity is found from the gradient of the displacement time graph. If, for example, the displacement is a sin curve then vel…
Mechanics
Conservation of momentum
…amount is constant throughout an interaction, such as a collision, provided that there are no external forces acting. Since velocity is a vector quantity, so too is momentum, and so momenum in the reverse direction will be negative. Key Concepts By…
Electricity and magnetism
Magnetic fields
…icular B field. A force acts on each individual charge within the field, depending on: flux density (B) in T charge (q) in C velocity at which the charge is moving (v) in ms-1 \(F=Bqv\) Your data booklet includes \(\sin \theta\) in this equation. Th…
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Rotational dynamics
…+2as\) \({\omega_f}^2={\omega_i}^2+2\alpha \theta\) \(\theta\) is angular displacement (rad) \(\omega_i\) is initial angular velocity (rads-1) \(\omega_f\) is final angular velocity (rads-1) \(\alpha\) is angular acceleration (rads-2) \(t\) is the ti…
Electricity and magnetism
Faraday's law
…ta\) \(\varepsilon\) is the EMF induced (V) \(B \) is magnetic flux density (T) \(L\) is the length of wire (m) \(v\) is the velocity of the wire (ms-1) \(\theta\) is the angle between the magnetic field lines and the normal (perpendicular) to the sw…
Circular motion and gravity
AHL Gravitational fields
…over r}-G{Mm\over r}=-{1\over 2}G{Mm\over r}\) NB: We bypassed a Data Booklet equation en route, which gives the size of the velocity for an orbtting body: \(v_\text{orbit}=\sqrt{G{M\over r}}\) Escape speed A ballistic object (i.e. a particle witho…
Mechanics
Equations of uniformly accelerated motion
…ill? Question 4 suvat 4: How long does it take for a ball to roll down a slope? Question 5 suvat 5: What is the release velocity when I juggle two balls? Just for Fun Which of these suvat equations are true and which are false? …
Mechanics
Balancing forces
…al forces no air to worry about Essentials Newton's First Law states that an object will remain at rest or at constant velocity unless acted upon by a resultant force. Using astronauts, we can see that a body will stay at rest or continue with…
Mechanics
Potential energy
…y to lift it at constant velocity. Work done = force x distance: \(F=Wh=mgh\) Remember when something is lifted at constant velocity the forces are balanced. No kinetic energy is gained. A common mistake is to think that 'mgh' is the general…
Circular motion and gravity
Centripetal force
…, the object moves along the tangent to the circle. Here is another example: Relationship between ω and v ω is the angular velocity = \(2\pi \over T\) v is the speed = \(2\pi r \over T\) From this we can deduce that \(v = ωr\) Essentials When…
Circular motion and gravity
Examples of circular motion
…motion, this will happen if the other end of the string is fixed. It´s not possible to make a vertical circle with constant velocity on the Earth because the mass is accelerated by gravity: At the top of the circle, weight will be adding to the tens…
Oscillations and waves
Standing waves on a string
…a narrow slit. Light, however, is polarised by a special Polaroid filter and not a slit. Summary Wave speed in a string The velocity of a wave in a string is related to the tension and mass per unit length of the string: \(v=\sqrt{T\over \mu}\) Diff…
10 IA ideas with toilet paper
…an advert involving a dog, soft, strong and very long. Unroll the paper down a long slope. What is the relationship between velocity and distance travelled? Ideal for an iterative model in Excel. 10. Football hooligan Hold the free end and throw the…
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Investigation ideas
…paratus Sonometer Driving the wire and resonance Changing wire Position of detector and driver Projectile launcher Range and velocity Range and angle Effect of air resistance Ball size and range Time of flight Trajectory (with camera) Maximum height…
Oscillations and waves
AHL Waves
…htarrow v=-\omega x_0\sin \omega t \) \(v=\pm \omega\sqrt{{x_0}^2-x^2}\) \(x_0\) is amplitude (m) \(t\) is time (s) \(v\) is velocity (ms-1) When an oscillating system is modelled as a mass on a spring, we can calculate the time period (and therefore…
Atomic, nuclear and particles
Wave particle duality
…0^{-34}\over 4\pi 1.2\times10^{-15}}\) \(\Delta p\geq4.4\times 10^{-20}\text{ kg ms}^{-1}\) Now estimating the consequential velocity of the electron reveals the impossibility of this position: \(v={p\over m}\) \(v={4.4\times 10^{-20}\over 9.11\times…
Electricity and magnetism
AC generators
…\(A\) is the perpendicular area of the coil in the field (m2) \(N\) is the number of turns on the coil \(\omega\) is angular velocity (rad s-1) \(t\) is time, with \(t=0\) for the coil sides rotating parallel to the field The maximum of this equation…
Electricity and magnetism
Current
…rrent from the following quantities: n, the number density of charge carriers A, the cross-sectional area v, the drift (net) velocity of charge carriers e, the charge on each charge carrier (electron) The resulting equation is: \(I = nAve\) Current i…
Oscillations and waves
Waves
…e. However, this is only noticeable when the surface is smooth. Refraction: When light passes from one medium to another its velocity changes resulting in a change of direction. A mathematical relationship can be used to calculate the angle of refrac…
Atomic, nuclear and particles
Nuclear physics
…stance of a approach when a positive alpha particle is fired at a nucleus. If the alpha particle has charge +2e, mass m and velocity v, the closest it will approach a nucleus of proton number Z is governed by the following equation: \(r={4kZe^2\over…
Exam questions
HL practice paper 2
…ge in potential energy can be calculated as follows: \(\Delta E_p=m\Delta V_g=m\times GM({1\over r_f}-{1\over r_i})\) Escape velocity A mass in orbit in a gravitational field possesses two types of energy: Kinetic energy due to its motion, \(E_k={1\o…
Mechanics
Distance and displacement
…ion of a particle using a displacement-time graph to show how the gradient and sign of the line relates to the direction and velocity of the particle. Test Yourself Use quizzes to practise application of theory. Displacement and distance 22/03/201…
Mechanics
Acceleration due to gravity
…eleration due to gravity is negative. Graphs of freefall A graph of displacement-time is an upside-down parabola. A graph of velocity-time is linear with negative gradient. Essentials Measuring the acceleration due to gravity is one of the sugges…
Basics
Scalars and vectors
…Some quantities have scalar and vector equivalents: Distance is a scalar and displacement is a vector Speed is a scalar and velocity is a vector Acceleration can be either (but is usually the consequence of a resultant force - vector) Essentials C…
Mechanics
Examples of forces
…t moving. Drag (F) Drag opposes the motion of bodies through a fluid. For slow moving bodies this is proportional to their velocity, v, but is proportional to v2 for fast ones. Drag force is also dependent on the size and shape of the body and the…
Mechanics
Newton's second law
…the resultant force acting on a body and its acceleration: \(F=ma\) Because acceleration is defined as the rate of change in velocity, Newton's second law can also be expressed as the rate of change of a momentum of a body is proportional to the…
Oscillations and waves
Oscillations
…x\) x (m) = displacement x0 (m) = amplitude ω (Hz) = angular frequency = 2πf t (s) = time a (ms-2) = acceleration v (ms-1) = velocity Energy changes As a pendulum swings or mass bounces on a spring, there is a continual exchange of energy from pote…
Oscillations and waves
Sound
…ressions. Reflection When a sound wave meets a wall, it pushes against the wall and the wall pushes back. Refraction The velocity of sound in air is related to temperature. If a sound passes from cold air to warm air, its direction will change. …
Electricity and magnetism
Moving charges in a magnetic field
…e derived by considering the moving charges in a wire: \(F=Bqv\) Essentials Since the force is always perpendicular to the velocity, the resulting motion is circular. Test Yourself Use quizzes to practise application of theory. Moving charges in…
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