Mechanics I

Level 3 Physics Study: Centre of Mass, Linear Momentum, Circular Motion I, Circular Motion II

an object’s ________ is where we can consider all of its mass to be

COM

an object will ________ if it COM moves beyond its base

rotate

________ occurs when an object recieves a force at its COM

translation

________ ________ occurs about the ________ when an object receives two forces either side of its COM

pure rotation, COM

x_com = ∑m_ix_i / ∑m_i for calculating the ________ from where you are measuring to the COM for any number of objects on a straight line

distance

if objects are not on a straight line, calculate the x and y components of distance to COM ________

separately

v_com = total ________ / total ________ = ∑m_iv_i / ∑m_i

momentum, mass

will v_com change if there is no net external force on the system?

no

________ is a change in momentum, ∆p

impulse

Newton’s __ st/nd/rd law states that an object will produce an ________ and ________ force on another object in a collision when no ________ external forces act, so ∆p₁ = ∆p₂. each individual object will experience a/an ________ but no change to the total ________ of the system

3, equal, opposite, net, impulse, momentum

a ________ diagram is used to calculate the impulse experienced by a single object in a collision, and will always have right angles or form an equilibrium triangle to enable calculations

vector

in uniform circular motion, ________ changes but ________ stays the same

velocity, speed

in uniform circular motion, a ________ force which is ________ is applied towards the centre of an object’s circuclar path (often friction or tension)

centripetal, unbalanced

an unbalanced F_c causes centripetal ________, which changes the directional component of ________

acceleration, velocity

if F_c is removed, an object travelling in circular motion will travel instead on a ________ path

tangential

for uniform circular motion, v = d / t where d = ___ = ________ and t = __ = ________

2πr, circumference, T, period

________ is the time taken for 1 complete rotation or revolution

period

a conical pendulum moves in a ________ circle, connected by a string which produces a cone shape to the motion of the system

horizontal

for a conical pendulum, __ is the mass which moves in a horizontal, circular path; θ is the angle between the string providing F_T and the ________ normal line; __ is the distance from the mass to the centre of its circular motion; and __ is the length of the string

m, vertical, r, L

for a conical pendulum, ________ forces (F_g = F_T(vertical) = F_T___θ) balance out, but the _______ force is unbalanced and provides centripetal force (F_c = F_{T(horizontal)} = F_T___θ)

vertical, cos, horizontal, sin

for a conical pendulum, F_T and F_g produce the ________ F_c

resultant

________ is a negligible force for most banked corner questions

friction

friction always ________ motion

opposes

there are two main forces to consider for a car travelling around a banked corner:

• F_{w_____} travelling ________ downwards

• F_r____ travelling ________ up from the road surface

weight, vertically, reaction, perpendicularly

F_reaction has two main components for a car travelling around a banked corner:

• F_r(vertical) balances out ________ and causes vertical forces to be in ________

• F_{r(horizontal)} is the r________ force and is u________, and supplies F_c without _______ needed

gravity, equilibrium, resultant, unbalanced, friction

for a car travelling too _______ around a banked corner, its motion will move up the road and friction will act down the road

fast

for a car travelling too _______ around a banked corner, its motion will move down the road and friction will act up the road

slowly

in _______ circular motion, both the velocity of and the forces experienced by an object change

vertical

in vertical circular motion, the feeling of “_______” is the _______ force, F_N, acting _______ to the surface it is on, while F_g = mg and always acts _______ downwards

weight, normal, perpendicular, vertically

at the _______ of vertical circular motion, F_g and F_N both act towards the centre of motion (_______)

F_c = F_N __ F_g

top, positive, +

F_Normal acts towards the centre of vertical circular motion and is always _______

positive

at the _______ of vertical circular motion, F_N acts towards the centre of motion (_______) while F_g acts vertically downwards (_______)

F_c = F_N __ F_g

bottom, positive, negative, -

at the _______ of vertical circular motion, F_N acts towards the centre of motion (_______); F_g acts vertically downwards, and θ is formed as the _______ angle between F_g and the line continuing F_N beyond the circle. on the F_g___θ component opposes F_N, while F_g___θ acts _______ to F_N and has no effect

F_c = F_N __ F_gcosθ

side, positive, smallest, cos, sin, perpendicular, -

at the top of vertical circular motion, F_N = __ and the object feels “weightless”

0

conservation of _______ can be applied for vertical circular motion

E_top = E_bottom

energy

at the top of vertical circular motion, F_c = F_N + F_g and F_N = __

F_c = F_g so mv²/r = mg, and __ can cancel

∴ v²_top = ___

at the bottom of vertical circular motion, E_top = E_bottom using conservation of ________

mgh_top + ½mv²_top = mgh_bottom + ½mv²_bottom

using h_top = __, v²_top = __, h_bottom = __, and __ can cancel:

2rg + ½rg = ½v²_bottom

∴ v²_bottom = ___

0, m, rg, energy, 2r, rg, 0, m, 5rg

the universal law of ________ states that F_g = GMm/r²

gravitation

for the universal law of gravitation, __ = universal gravitational ________, 6.67×10^-11 Nm²kg^-2

G, constant

for the universal law of gravitation, M is ________ than m, and both are measured in __

larger, kg

for the universal law of gravitation, r is the ________ distance between the ___’s of M and m - make sure to include the ________ of each object!

radial, com, radius

M and m experience ________ ________ (the same / a different) gravitational force, F_g

the same

Earth’s gravitational field strength increases ________ from the centre to the surface of the Earth, then ________ as an inverse square once beyond Earth’s surface

linearly, decreases

the gravitational field around Earth is ________, and is ________ where the lines are closest together (at Earth’s surface)

radial, strongest

Earth’s gravitational field is assumed to be ________ at Earth’s surface

parallel

combining weight and gravity, F_w = F_g

mg = GMm/r², and __ can cancel

g = GM/r²

on Earth’s surface, G, M and r are all _______; therefore, _______ due to gravity, g, is independent of individual _______!

m, constants, acceleration, mass

when an object is in a/an _______, F_c = F_g

mv²/r = GMm/r², and m and r can cancel

v² = GM/r

also, since an orbit assumes uniform _______ motion, v = d/t = 2πr/T

G and M are both _______, and remember that r is the sum of Earth’s _______ and the _______ of the orbit!

orbit, circular, constants, radius, height

a satellite holds its position relative to Earth in a _______ orbit, which requires:

• the right h_______ and s_______

• T = __ h

• must be above the _______, rotating in the same _______ as Earth

geosynchronous, height, speed, 24, equator, direction

at the _______, F_N = F_g since an object only rotates; at the _______, F_N + F_g = F_c, since an object has a _______ centripetal force as it moves in a full circular path every __ h due to Earth’s rotation

poles, equator, resultant, 24

Kepler’s laws state that:

1. all planets move in _______ orbits with the _______ at one focus

2. the _______ formed between two lines between the planet and the Sun and the planet’s orbital path is _______ for equal _______ intervals

3. the square of the period, T², is _______ to the cube of the semimajor axis of its orbit, r³

• the radial line and tangent are not _______, meaning that a component of force could change an object’s speed

elliptical, Sun, area, equal, time, proportional, perpendicular

to prove Kepler’s 3rd law: GMm/r² = ma (for F_g)

a is _______, so a = v²/r, and __ can cancel, so GM/r² = v²/r

v = 2πr/T so GM/r² = 4π²r²/T²r

rearranging, GM x T² = 4π² x r³, so T² is _______ to r³

remember to fully expand (2πr/T)²!

centripetal, m, proportional