Physics: Measurement, Kinematics, Dynamics, Forces

R = X + Y or X - Y

ΔR = ΔX + ΔY

R = X*Y or X/Y

ΔR/R = ΔX/X + ΔY/Y

R = kX, where k is a constant

ΔR = kΔX. [NOTE: constants dont appear in fractional uncertainty because they get canceled out.]

R = X^p

ΔR/R = |p|*ΔX/X

6 basic units

meter, second, kilogram, kelvin, ampere, mol

systematic error

affect accuracy, values away from true value by a consistent value

random error

affect precision, values are scattered around the true value

conditions for equations of motion to apply

uniform acceleration, straight line

linear momentum

product of the mass of an object and its velocity. p = m*v

N2L

Fnet = dp/dt = d(mv)/dt

POCOM

total momentum of the system remains the same, provided no resultant external force acts on the system. m1u1 + m2u2 = m1v1 + m2v2

elastic collision

total KE of the system is conserved bfr and aft the collision. u1 + v1 = u2 + v2

RSOA = RSOS

u1-u2 = v2-v1

equilibrium condition

resultant force about any direction and resultant torque about any axis of rotation must be zero. ∑Fy = 0, ∑Fx = 0.

moment

produce of force and perpendicular distance from the pivot to the line of action of force. τ = F x d⊥

velocity

rate of change of displacement

general reminders for forces questions

resolve forces horizontally and vertically (or parallel and perpendicular if got slope)

always state N2L or N3L.

state sign convention.

uncertainty for complex eqn

ΔR = (Rmax - Rmin)/2

how to reduce random error

take average of repeated measurements, plot a best fit line

How to reduce systematic error

plot best fit line, if got vertical intercept for a directly proportional rsp, then theres a systematic error present.

kinematics equations

v = u + at

s = 1/2(u+v)t

N3L

action reaction pair: equal magnitude, opposite direction, two opposite bodies, same type of force.

Impulse-Momentum Theorem

change in momentum, area under F-t graph, = Δp/Δt

spring force / hooke's law

F = kx, x is the extension of the spring

inelastic collision

masses move with same final velocity. m1u1 + m2u2 = (m1+m2)V

application of Impulse-Momentum Theorem: airbags in car

1. when car suddenly stops, passenger continues moving due to inertia

2. the Δ in p is the same w or w/o the airbag

3. when airbag is activated, time taken, Δt, for the passenger to come to a rest increases.

4. from IMT, = Δp/Δt, thus average force decreases, reduces likelihood of serious injuries

force IMT qns, focus on constant Δp and longer Δt to ↓

resolve weight on slope

//: mgsin𝚹 ⊥: mgcos𝚹

In elastic collisions, both p and ke are conserved in the collision. T/F

F: p is conserved. KE is NOT conserved throughout the collision. HOWEVER, KEi = KEf.

rotational eqb questions

state which pivot your taking moments about.

acw = cw

centre of mass formula

∑mixi/∑mi. pick a reference point. x1 = dist b/w m1 and ref pt.

lines of action of forces pass through a common pt

only when obj in eqb is acted on by THREE non-parallel forces

torque

torque of a couple is the product of one of the forces and the perpendicular distance between the two forces

Keff for springs in parallel

Keff = ∑k

Keff for springs in series

[1/k1 + 1/k2 + …]^-1

upthrust

upward force, acts from centre of gravity of displaced fluid, aka centre of buoyancy

conditions to use kinematics equations

linear motion. constant acceleration

v-t graph for call bouncing

a-t graph for bouncing ball