Course

A2 Physics: Circular Motion, Gravitation and Oscillations (9702)

Name: A2 Physics: Circular Motion, Gravitation and Oscillations (9702)
Price: 1999 BDT

9702 topics 12, 13 and 17. A ball on a string, a planet in orbit and a mass on a spring turn out to be one problem: an acceleration that always points at a centre.

43 lessons4h 21mEnglish

What you'll learn

Measure an angle in radians and see why every circular-motion formula assumes them
Explain why a body moving at constant speed is still accelerating, and where that acceleration points
Treat centripetal force as a resultant of forces you already know, never as a new one
Use the inverse-square law for gravitational field strength, and the 1/r form for potential
Recognise s.h.m. from a = -w^2 x, and read energy off a displacement graph

Requirements

AS topic 3, dynamics: F = ma, and resolving a resultant force
AS topic 5: kinetic and potential energy, and work as force times distance
O Level trigonometry: sine and cosine of an angle, and the radian is taught here from scratch
Comfortable rearranging a formula with a square or a square root in it

Course content

43 lessons · 4h 21m

12.1-12.2 · Motion in a circle

The radian, angular speed, and the one acceleration that changes direction without changing speed. Centripetal force turns out to be the resultant of forces you already know, and nothing is thrown outwards.

0/13

An angle measured by arc length

Wrap the radius around the rim and count how many times it fits.

Preview5m 2.

Angular speed is angle per second

A turning wheel goes nowhere in a straight line, so measure the angle instead.

Preview6m

Same angle, different speed

Two points on one wheel share an angular speed but not a speed. Find the link.

Constant speed, changing velocity

Subtract two velocity arrows and read where the difference points.

Where a = v²/r comes from

The velocity triangle turns through the same angle as the ball, and that gives a.

The force that keeps it turning

A 0.50 kg ball, a 2.0 m string, and a tension of 36 N. Find the breaking speed.

Centripetal force is a resultant

Three forces act on a turning auto-rickshaw. None of them is labelled centripetal.

Nothing is thrown outwards

Cut the string and watch where the ball actually goes. Then explain the seat.

Deducing F = mv²/r from a graph

Tension against speed is a curve. Plot the right quantity and it straightens.

10.

The conical pendulum

A bob on a string sweeps a cone. Resolve the tension and the mass cancels out.

11.

The banked track

Tilt the road and no friction is needed. The same tan θ = v²/(rg) reappears.

12.

One exam question, end to end

Seven marks, three parts, no options: acceleration, resultant force, then what actually provides it.

13.

Circular motion: quick revision

Reconnect angular motion, centripetal acceleration and the real forces that provide the inward resultant.

13.1-13.4 · Gravitational fields

One inverse-square law for every pair of masses. Field strength that is also the acceleration of free fall, a potential that is always negative, the speed needed to escape, and the orbit that holds a satellite over one spot on the ground.

0/15

Field strength is force per unit mass

The same ball falls three different ways. The ball did not change, the place did.

Preview5m 2.

One law for every pair of masses

Double the distance and the pull is not halved. Find out what it becomes.

Preview6m

The two pulls are always equal

The Earth pulls the satellite, and the satellite pulls the Earth just as hard.

Reading g off the curve

g = GM/r² plotted against distance from the centre, from the ground to orbit.

Why 9.8 N/kg equals 9.8 m/s²

The heavy stone is pulled harder and still lands with the light one. Explain that.

Why potential is always negative

Put the zero at infinity and every other point in the universe sits below it.

Where gravity actually peaks

GM/r squared says the field grows without limit toward the centre. It is zero there, and the peak sits at the surface.

Potential energy and the area under the curve

Where the −GMm/r comes from, and where the familiar mgh fits inside it.

Gravity as the centripetal force

Launch a satellite too slowly and it lands. Find the speed a circle needs.

10.

A wider orbit takes longer

Twice as far out is not twice as slow. Stretch the orbit and read the period.

11.

The orbit that stays above one spot

Every dish on every roof is bolted still. Work out the radius that allows it.

12.

The speed that never comes back

A marble and a rocket need exactly the same escape speed. Find out why.

13.

The total energy of a satellite

Kinetic and potential energy combine into one negative total, half the size of Ep, that rises with a higher, slower orbit.

14.

One exam question, end to end

Eight marks, three parts, no options: field strength, orbital speed, then a potential energy whose sign carries a mark.

15.

Gravitational fields: quick revision

Reconnect field, potential and orbital motion, then rehearse signs and orbit reasoning.

17.1-17.3 · Oscillations

One condition, a = −ω²x, produces every graph in this chapter. Displacement, velocity and acceleration and the phase between them, the speed at any displacement, the energy that swaps back and forth, damping, and the resonance a driver can build.

0/12

Amplitude, period, frequency

Change the mass of a pendulum and the period ignores you. Find what it listens to.

Preview5m 2.

The condition a = −ω²x

Where is the acceleration largest, and what is the minus sign doing there?

Preview6m

Why the graph is a sine curve

Track only the height of a point going round a circle, and read what it traces.

Displacement, velocity, acceleration

Three curves with one period that never peak together. Read the phase differences.

Speed at half the amplitude

Half the displacement does not give half the speed. Derive what it does give.

Kinetic and potential, swapping

Predict the energy split at half the amplitude, then watch the two bars move.

The energy graphs the exam asks for

Two parabolas and a flat line. Sketch them before you see them.

Light, critical and heavy damping

Three systems released from the same point. Predict which settles first.

Driving at the natural frequency

Sweep the driving frequency until small pushes build a very large amplitude.

10.

What damping does to the peak

Amplitude against driving frequency, with a damping slider under the peak.

11.

One exam question, end to end

Seven marks, three parts, no options: angular frequency, maximum speed, then the speed halfway out.

12.

Oscillations: quick revision

Reconnect SHM, energy, damping and resonance, then repair the displacement-speed shortcut.

About the creator

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