• Inertial Mass, Gravitational Mass and Weight

    We mislead ourselves when we say we are measuring the mass of an object. If fact we are measuring the force of gravity on that object and changing that force into a mass using a calibrated scale. If we were to 'measure' the mass of an object at...

    https://astarmathsandphysics.com/ib-physics-notes/mechanics/1371-inertial-mass-gravitational-mass-and-weight.html

  • Instantaneous Average

    Speed is not merely distance divided by time. Intuitively we mean the distance travelled in a particular time divided by the time taken to travel that distance. The calculated speed will be the average speed over that time interval, but the speed may...

    https://astarmathsandphysics.com/ib-physics-notes/mechanics/1372-instantaneous-average.html

  • Kepler's Third Law

    Kepler's laws of motion describe the orbits of planets around the Sun. They were were a bridge between the Aristotlean view of the Solar System, which described in error and did not explain, and the Newtonian view, which described (almost) correctly...

    https://astarmathsandphysics.com/ib-physics-notes/mechanics/1373-kepler-s-third-law.html

  • Momentum

    Linear Momentum – units kg m/s - is defined as the product of mass and velocity. It is a vector, and is of fundamental importance because in any collision or any isolated system it is conserved as a consequence of Newton's third law. We can write this...

    https://astarmathsandphysics.com/ib-physics-notes/mechanics/1374-momentum.html

  • Newton's Second Law of Motion

    Newtons first law of motion states that a body subject to no net external forces continues in a state of uniform motion. His second law of motion in a sense makes his first law complete by telling us what will happen in the event of a body being...

    https://astarmathsandphysics.com/ib-physics-notes/mechanics/1375-newton-s-second-law-of-motion.html

  • Newton's Third Law of Motion

    Newton's third law states: To every action there is an equal and opposite reaction. Newton's third law implies that forces always come in pairs. In fact, these force pairs have the same origin and nature. If one is gravitational, then so is the other;...

    https://astarmathsandphysics.com/ib-physics-notes/mechanics/1376-newton-s-third-law-of-motion.html

  • Some Basics of Forces

    Forces occur whenever the direction of motion of a body changes – it accelerates - or whenever an object changes shape. When a football is kicked for example, the ball may change shape slightly – temporarily – and will change direction – often towards...

    https://astarmathsandphysics.com/ib-physics-notes/mechanics/1377-some-basics-of-forces.html

  • The Approximate Expression for the Gravitational Potential Energy

    The equation (increase in) Gravitational Potential Energy= is only an approximation when is is small compared to the radius of the Earth. The graph of gravitational potential against the distance from the Earth's centre is shown below. To move from a...

    https://astarmathsandphysics.com/ib-physics-notes/mechanics/1378-the-approximate-expression-for-the-gravitational-potential-energy.html

  • Torque and Moments

    The motion of a rigid body is in general a combination of translation and rotation. The two tyopes of motion can be treated independently. A translation takes place when every particle in a rigid body has the same velocity while a rotation is when...

    https://astarmathsandphysics.com/ib-physics-notes/mechanics/1379-torque-and-moments.html

  • Uniform Circular Motion

    The phrase 'uniform circular motion' describes planar motion in a circle at constant speed. If the motion takes place on the Earth, this almost certainly means that the motion is horizontal. For example a mass suspended at the end of a string may be...

    https://astarmathsandphysics.com/ib-physics-notes/mechanics/1380-uniform-circular-motion.html

  • Uniformly Accelerated Motion

    If the acceleration of a body is uniform or constant, simplifications become possible so it is important to determine if the acceleration is uniform to a good approximation. Possible methods of finding if the acceleration of a body is uniform include:...

    https://astarmathsandphysics.com/ib-physics-notes/mechanics/1381-uniformly-accelerated-motion.html

  • Velocity Time Graphs

    Velocity times graphs indicate the velocity as a function of time. One direction is taken as positive and one direction is taken as negative, so only this forwards and backwards motion can be displayed. At any time t the velocity can be read of the...

    https://astarmathsandphysics.com/ib-physics-notes/mechanics/1382-velocity-time-graphs.html

  • Weight

    Weight and mass are often taken to be synonymous. In fact they are very different concepts, but people are easily confused because although weight is actually a force measured in newtons and mass is the amount of matter measured in kg, people often say...

    https://astarmathsandphysics.com/ib-physics-notes/mechanics/1383-weight.html

  • Weightlessness

    One way of defining the weight of an object is to say that the weight is the value of the force recorded on a supporting scale. If the scales were set up in a lift, the value they record would depend on the magnitude an direction of the acceleration of...

    https://astarmathsandphysics.com/ib-physics-notes/mechanics/1384-weightlessness.html

  • Work Done by a Force

    A force is done whenever the point of application of the force moves in the direction of the force. If a force pushes a block then the block does work. The work done by the force however is not in general to the force multiplied by the distance. Only...

    https://astarmathsandphysics.com/ib-physics-notes/mechanics/1385-work-done-by-a-force.html

  • Canonical Transformations

    Coordinate transformations or changes of variables are useful because a suitable choice of coordinates or variables can dramatically simplify a problem. For example cannot be evaluated by inspection but on using the integral becomes on using the...

    https://astarmathsandphysics.com/university-physics-notes/classical-mechanics/1517-canonical-transformations.html

  • An Example of a Time Dependent Hamiltonian and Lagrangian

    Deriving the Hamiltonian and Lagrangian for a time dependent system is not much more complicated than for the time independent case. The pendulum of mass and length below is made to oscillate at A with the distance OA given by The potential energy is...

    https://astarmathsandphysics.com/university-physics-notes/classical-mechanics/1518-an-example-of-a-time-dependent-hamiltonian-and-lagrangian.html

  • Equations of Curcular Motion

    For motion in a straight line with constant acceleration, we can use the SUVAT equations of motion: These have exact equivalents for motion in a circle with constant angular acceleration. In these equations, and We can derive the circular equations of...

    https://astarmathsandphysics.com/university-physics-notes/classical-mechanics/1519-equations-of-curcular-motion.html

  • Finding a Generating Function From a Given Canonical Transformation

    Generating functions have many uses and it is useful to be able to construct one from a given transformation. We can do this from the defining relationship between the generating function and the transformation. Example Show that the transformation is...

    https://astarmathsandphysics.com/university-physics-notes/classical-mechanics/1520-finding-a-generating-function-from-a-given-canonical-transformation.html

  • Generalized Coordinates

    In order to describe the motion of a system mathematically we need to be able to specify the instantaneous configuration of the system - the position. For example the motion of a projectile can be specified by the horizontal distance of the projectile...

    https://astarmathsandphysics.com/university-physics-notes/classical-mechanics/1521-generalized-coordinates.html

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