A level Physics Notes
Circular Motions
Circular Motions Special Cases
1. 1 Radian (rad) is the angle turned from the center
of the circle when the object travelled an arc of
equal length to the radius of the circle
 𝐷𝑒𝑔𝑟𝑒𝑒𝑠 × 𝜋⁄180 = 𝑟𝑎𝑑
2. Time period – time taken to complete 1 circle
3. Frequency – number of cycles completed per
second
4. RPM - Revolutions per minute
5. Centripetal force – force acting towards the
center of a circular motion
6. Angular velocity – angle turned per seconds
 𝜔 = 𝜃⁄𝑡 = 2𝜋⁄𝑡 = 2𝜋𝑓
7. Velocity is always changing as direction is always
changing
 𝑣 = 𝜔×𝑟
8. Since velocity is changing, there must be an
acceleration
2
 𝑎 = 𝑣 ⁄𝑟 = 𝜔2 × r
2
 𝐹 = 𝑚𝑣 ⁄𝑟 = 𝑚𝜔2 r
Gravitational Fields
1. Field of force – when two objects are not touching
but cause a force on one another
2. Gravitational field – area of space where a mass
experience a force
3. Field lines – points in direction a “test mass” would
move
 Closer lines means stronger fields
4. When the distance between any 2 object is much
bigger than the object themselves, we consider
them point masses
5. Gravity is always an attractive force.
6. Uniform field has parallel, equally spaced field lines
7. Newton’s Gravitational Law – any 2 point mass
attracts each other with a force proportional to
their masses and inversely proportional to the
square of their separation
 Gravitational constant = 6.67 x 10-11 Nm2Kg-2
 𝐹 = 𝐺𝑀𝑚⁄𝑟 2
Geostationary
Oscillations
1. Humpback Bridge
2. Vertical Circle
3. Spinning at an angle
Vertical component:
𝑇𝑠𝑖𝑛(𝜃) = 𝑚𝑔
Horizontal component:
2
𝑇𝑐𝑜𝑠(𝜃) = 𝑚𝑣 ⁄𝑟
𝑔𝑟
 𝑣 = √ ⁄tan(𝜃)
8. Field strength – gravitational force per unit mass
on a small test object placed at a point
 𝑔 = 𝐹⁄𝑚
 Negative gradient of potential graph
9. Using the equation in 7 and 8, we can find the
field strength of a mass M
 𝑔 = 𝐺𝑀⁄𝑟 2
10. Gravitational Potential – work done in moving a
unit mass from infinity to a point or potential
energy per unit mass (negative energy)
 Energy is required to allow the object to have 0
Joules (become free)  𝜙 = − 𝐺𝑀⁄𝑟
 Energy of small object of mass in this potential:
𝑔𝑝𝑒 = 𝜙 × 𝑚 = −𝐺𝑀𝑚⁄𝑟
2
11. Orbit. 𝐹 = 𝐺𝑀𝑚⁄𝑟 2 = 𝑚𝑣 ⁄𝑟 𝑣 2 = 𝐺𝑀⁄𝑟
12. Kepler’s 3rd law
2
2
 (2𝜋𝑟⁄𝑡)2 = 𝐺𝑀⁄𝑟  𝑇 ⁄𝑟 3 = 4𝜋 ⁄𝐺𝑀

1. Oscillation – back and forth motion around an equilibrium point
2. Free Oscillation – no external force/energy acts on the system
3. Forced Oscillation – An external force/oscillation is applied to the
system
4. Formula booklet

 𝑎 = −𝜔2 𝑥 (simple harmonic motion)

 𝑣 = 𝑣0 cos(𝜔𝑡)
Weightlessness
 𝑣 = ±𝜔√𝑥0 2 − 𝑥 2
 Is the result of a perfect orbit
5. Simple harmonic motion – motion where acceleration is proportional
 Since gravity is providing a
in magnitude (𝑎 ∝ 𝑥) and in opposite direction to the displacement
centripetal force pulling the
(𝑎 ∝ −𝑥 )from a fixed point.  𝑎 = −𝜔2 𝑥
space ship around and the
 Maximum acceleration = −𝐴𝜔2
person in the ship is “falling”
with an acceleration of g, the 6. Displacement at any given time from
 Equilibrium point = 𝐴 sin(𝜔𝑡)
person in space will feel no
 Maximum displacement =
contact force with the
ground thus weightlessness. 7. Velocity at any point:
 Gradient of displacement – time graph (tangent to a point)
 Using formula from the booklet (above)
 The velocity is maximum at the rest point 𝑣0 = 𝜔𝑥0
Orbit time is the same as
earth (1 day) so is always in
same position in space in
relative to earth
Position is above equator
Moves from West  East
Energy in the system
Resonance



In real life, some energy is lost and the object will stop
accelerating
Damping – when energy is lost from the system causing the
amplitude of motion to decrease
 Light : object oscillated but slowly losses amplitude, not at a
steady rate – at an exponential rate (E.g. air resistance)
 Heavy : object can not oscillate, slowly return to equilibrium
(E.g. in oil)
 Critical : Stops the oscillation at fast as possible – 1/4 of an
oscillation (E.g. Car suspension)

When the frequency of the force
applied is equal to the natural
frequency of the free oscillation
 Resulting in a dramatic increase
in amplitude of oscillations
Damping reduces the amplitude and
frequency of the resonance.