#### The Approximate Expression for the Gravitational Potential Energy

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 distance say, near to the Earth's surface to a distance we need to put in an amount of...

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

his normal weight (below left). If the lift accelerates upwards with acceleration he experiences his weight doubling (above centre). If the cable holding the lift breaks, ignoring air resistance, the lift and the man in it would accelerate down with an...

https://astarmathsandphysics.com/ib-physics-notes/mechanics/1384-weightlessness.html#### The Mass Spectrometer

of the particle always, so forces the particle to move in a circle. The centripetal force – the force acting towards the centre of the circle – is Equating the magnetic to the centripetal force gives Rearrangement of this gives If the ions have the same...

https://astarmathsandphysics.com/ib-physics-notes/quantum-and-nuclear-physics/1432-the-mass-spectrometer.html#### The Photoelectric Effect - Finding Planck's Constant

The photons of light on the left and have enough energy to eject a photon from the metal plate, but the photon in the centre does not. The equation governing the photoelectric effect is (1) where is the maximum kinetic energy of the emitted electrons...

https://astarmathsandphysics.com/ib-physics-notes/quantum-and-nuclear-physics/1434-the-photoelectric-effect-finding-planck-s-constant.html#### Area of Circles Filling a Sector

\rightarrow r= \frac{10}{3} cm\] . The smaller circles extend out to \[10-2r=10- 2 \frac{10}{3}=\frac{10}{3} cm \] from the centre. Repeating the above process for the next largest circle gives us a radius for this circle of \[\frac{1}{3} \frac{10}{3} =...

https://astarmathsandphysics.com/ib-maths-notes/trigonometry/5001-area-of-circles-filling-a-sector.html#### Interference

constructive interference. The resulting wave is larger than either wave. If the waves are out of phase everywhere (below centre) then they have the same wavelength and we have destructive interference. The resulting wave has zero displacement...

https://astarmathsandphysics.com/ib-physics-notes/waves-and-oscillations/1490-interference.html#### Jupiters Great Red Spot

is increasing, possibly as a result of shrinking. At the edge of the spot the wind speed is up to 430 km/h, but at the centre the wind speeds are close to zero. Infrared data indicates that the spot is colder and about 8 km higher altitude than most of...

https://astarmathsandphysics.com/university-physics-notes/planetary-science/1507-jupiters-great-red-spot.html#### Sunspots

Sun's interior decreases; and with it surface temperature. A sunspot is actually a depression in the Sun's surface. At the centre is the dark umbra, where the magnetic field is radially out from the Sun, and surrounding is the lighter penumbra where the...

https://astarmathsandphysics.com/university-physics-notes/astronomy/1509-sunspots.html#### Using the Biot - Savart Law to Find the Magnetic Field on the Axis of a Circular Loop

and hat r is the unit vector in the direction of For the point on the axis of the current loop above and Hence When at the centre of the coil,

https://astarmathsandphysics.com/university-physics-notes/electricity-and-magnetism/1554-using-the-biot-savart-law-to-find-the-magnetic-field-on-the-axis-of-a-circular-loop.html#### The Basics of Simple Harmonic Motion

Simple harmonic motion occurs when motion in a circle with uniform acceleration is projected on a line through the centre of the circle. The motion is most naturally projected onto the x and y axes. Suppose the motion is projected onto the – axis. Then...

https://astarmathsandphysics.com/a-level-maths-notes/m3/3629-the-basics-of-simple-harmonic-motion.html#### Elastic Strings

stored in a stretched spring by integration. Because we may also write Tension is a string is always directed towards the centre of the string, and has the same magnitude at each point of the string. If the string is fixed at one end to a surface with...

https://astarmathsandphysics.com/a-level-maths-notes/m3/3639-elastic-strings.html#### Lamina Suspended at Angle to Horizontal

of a side from a vertex and the other at a vertex, so that the topmost side AB is at an angle to the horizontal. The centre of gravity O is two thirds of the distance from A to the midpoint of the side BC, and and the line from A to the midpoint of BC...

https://astarmathsandphysics.com/a-level-maths-notes/m3/3640-lamina-suspended-at-angle-to-horizontal.html#### Multi Stage Rockets

stage. Suppose that when the booster is discarded the speed of the rocket is u and the rocket is a distance R from the centre of the Earth. Take the mass of the unit as The force of gravity where is the mass of the Earth is the only force acting so...

https://astarmathsandphysics.com/a-level-maths-notes/m3/3646-multi-stage-rockets.html#### Particle Moving in a Horizontal Circle Attached to Two Rods

in a horizontal circle, will produce forces in the rods which balance vertically and produce a force directed towards the centre of the circle which keep the partilce moving in the circle. We can find the forces in the rods by resolving vertically and...

https://astarmathsandphysics.com/a-level-maths-notes/m3/3647-particle-moving-in-a-horizontal-circle-attached-to-two-rods.html#### Particle on String Executing Circular Horizontal Motion

we have to use the fact that the acceleration for a particle moving in a circle is of magnitude or and directed towards the centre of the circle. We apply (2) (2) divided by (1) gives Then Unlike as in simple harmonic motion the period does depend on...

https://astarmathsandphysics.com/a-level-maths-notes/m3/3649-particle-on-string-executing-circular-horizontal-motion.html#### Sphere Attached to a String Resting Against a Smooth Wall

gives (2) Taking moments about B gives (3) Equating (1) and (3) gives so that the line of action of passes through the centre of the sphere.

https://astarmathsandphysics.com/a-level-maths-notes/m3/3654-sphere-attached-to-a-string-resting-against-a-smooth-wall.html#### How Fidget Spinners Work

fidget fidget spinner is a toy that you can set spinning b holding the centre between two fingers and giving the rim a push. When the fidget spinner starts to spin, it has angular momentum, with magnitude given by \[J= \omega I\] , directed...

https://astarmathsandphysics.com/a-level-maths-notes/m3/4698-how-fidget-spinners-work.html