Circular motion and gravitational field by AE19F MUHD NAQIB

muhdnaqib — 2020-05-20 09:58:28 UTC

*Concise notes
(By Muhammad Naqib Bin Salim)

arrazosuparjo — 2020-05-21 00:02:56 UTC

Orbiting Under Gravity

arrazosuparjo — 2020-05-21 00:04:51 UTC

For an object orbiting a planet, such as an artifiicial satellite
orbiting the Earth, gravity provides the centripetal force
which keeps it in orbit

arrazosuparjo — 2020-05-21 00:28:59 UTC

To calculate the speed at which an object has to move to stay in the circular motion

Centripetal Force, F

arrazosuparjo — 2020-05-21 00:29:00 UTC

The Centripetal Force is Equal to the Force between two point masses

THE ORBITAL PERIOD

arrazosuparjo — 2020-05-21 00:40:18 UTC

the time taken for a
complete orbit, the orbital period T

arrazosuparjo — 2020-05-21 00:51:58 UTC

To find the T

arrazosuparjo — 2020-05-21 00:51:58 UTC

Substitute the v as v^2

arrazosuparjo — 2020-05-21 01:11:54 UTC

The square of the period is directly
proportional to the cube of the radius

ORBITING THE EARTH

arrazosuparjo — 2020-05-21 01:13:39 UTC

arrazosuparjo — 2020-05-21 01:25:23 UTC

In order for a satellite to maintain a
particular orbit, it must travel at the correct speed

Observing The Earth

arrazosuparjo — 2020-05-21 01:37:46 UTC

Functions of satellites

COMMERCIAL

arrazosuparjo — 2020-05-21 01:39:20 UTC

METEOROLOGICAL

arrazosuparjo — 2020-05-21 01:39:51 UTC

MILILITARY

arrazosuparjo — 2020-05-21 01:40:01 UTC

ASTRONOMICAL OBERSVATIONS

arrazosuparjo — 2020-05-21 01:40:18 UTC

NAVIGATION

arrazosuparjo — 2020-05-21 01:40:29 UTC

TELECOMMUNICATION

arrazosuparjo — 2020-05-21 01:40:36 UTC

muhdnaqib — 2020-05-21 04:40:10 UTC

EXAMPLES

Geostationary Orbit

arrazosuparjo — 2020-05-21 05:00:00 UTC

A special type of orbit is one in which a satellite is
positioned so that, as it orbits, the Earth rotates below
it at the same rate.

Telecommunications

arrazosuparjo — 2020-05-21 05:06:00 UTC

Television Broadcasting

arrazosuparjo — 2020-05-21 05:06:20 UTC

arrazosuparjo — 2020-05-21 05:10:01 UTC

A base station
on Earth sends the TV signal up to the satellite, where it
is amplified and broadcast back to the ground

Determine the distance of a satellite in Geostationary Orbit using the equation ;

arrazosuparjo — 2020-05-21 05:12:19 UTC

CIRCULAR MOTION

muhdnaqib — 2020-05-21 06:58:38 UTC

muhdnaqib — 2020-05-21 07:10:03 UTC

Problem solving
(Questions and Answers)

CENTRIPETAL ACCELERATION AND CENTRIPETAL FORCE

muhdnaqib — 2020-05-21 07:37:58 UTC

muhdnaqib — 2020-05-21 07:42:37 UTC

muhdnaqib — 2020-05-21 07:47:24 UTC

EXAM STYLES QUESTION

Describing Circular Motion

vivinia7788 — 2020-05-21 08:29:09 UTC

Things that move in circle.

8.1 (a(i)) - understanding concept gravitational as an e.g of a field of force

izazizahariman — 2020-05-21 08:35:31 UTC

- spacing between field line = strength of gravitational field

- line inward = all objects attracted to centre of earth

The wheels of bicycle

vivinia7788 — 2020-05-21 08:38:35 UTC

The moon in its orbit around the Earth

vivinia7788 — 2020-05-21 08:43:01 UTC

The hands of a clock

vivinia7788 — 2020-05-21 08:46:42 UTC

or maybe it can be... Mr Bean moving in circle in a washing machine!

vivinia7788 — 2020-05-21 08:51:34 UTC

8.1 (a(ii)) defining GF strength as "force/mass"

izazizahariman — 2020-05-21 08:53:43 UTC

-Gravitational field strength is the gravitational force exerted per unit mass on a small object placed at a point

Angular Displacement θ is :

vivinia7788 — 2020-05-21 08:56:02 UTC

The angle θ through which the object has moved

8.2 (b) Newton's law of gravitation

izazizahariman — 2020-05-21 09:07:50 UTC

Angles in Radians

vivinia7788 — 2020-05-21 09:08:39 UTC

It is more
convenient to measure angles and angular displacements
in units called radians rather than in degrees.

Defining radians

vivinia7788 — 2020-05-21 09:12:29 UTC

One radian is the angle subtended at the centre of a circle
by an arc of length equal to the radius of the circle.

izazizahariman — 2020-05-21 09:12:41 UTC

Conversion between Radians and Degrees

vivinia7788 — 2020-05-21 09:20:40 UTC

8.2 (c) Inverse square law field

izazizahariman — 2020-05-21 09:23:04 UTC

- if the distance doubled 2x, lines are spread out over 4x the surface area

Steady Speed, changing Velocity

vivinia7788 — 2020-05-21 09:28:13 UTC

Speed - Scalar quantity (magnitude only)
Velocity - Vector quantity (magnitude + direction)

The arrows are straight and show the direction of motion at a particular instant. They are drawn as tangents to the circular path. As the object travels through points A, B, C, etc., its speed remains constant but its direction changes. Since the direction of the velocity v is changing, it follows
that v itself (a vector quantity) is changing as the object moves in a circle.

Angular Velocity

vivinia7788 — 2020-05-21 09:38:14 UTC

We use the symbol ω (Greek letter omega) for angular
velocity, measured in radians per second (rads−1).

solve problems using g=GM/r^2

izazizahariman — 2020-05-21 10:03:33 UTC

Gravitational potential

izazizahariman — 2020-05-21 10:09:03 UTC

- is the work done per unit mass in bringing a mass from infinity to a point

- greek letter phi = symbol for potential

- gravitational potential is ALWAYS -ve because mass is brought towards another mass. gpe decreases. gpe at infinity = 0 anywhere else gpe and potential are <0.

solving gravitational potential

izazizahariman — 2020-05-21 10:26:52 UTC