Title: InkMaths / Mechanics essentials
On every note of this deck, unless a note says otherwise:
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Front: SPOT THE ERROR
Say what is wrong with this claim:
At the top of its flight, a projectile's acceleration is zero.
Back: Only the vertical velocity is zero at the apex. Gravity acts all flight long, so the acceleration is 9.8 m s⁻² downwards there, the same as everywhere else.

Front: DEFINE
Define: limiting equilibrium.
Back: The state in which an object is still in equilibrium but on the point of slipping, so friction has reached its maximum value μR.

Front: STANDARD RESULT — LEARN IT
Projectile components:
u at angle θ ⇒ ?
Back: u cos θ across, u sin θ up

Front: SPOT THE ERROR
Say what is wrong with this claim:
A moving object must have a force pushing it along.
Back: Newton's first law says the opposite: with no resultant force, motion simply continues. Forces change velocity; they are not needed to keep it. What slows real objects is a real backward force, friction or resistance.

Front: DEFINE
Define: uniform beam.
Back: A beam whose mass is evenly spread, so its whole weight can be modelled as acting at its midpoint.

Front: STANDARD RESULT — LEARN IT
Weight on a slope:
components of mg on a slope at θ: ?
Back: mg sin θ along, mg cos θ into

Front: STANDARD RESULT — LEARN IT
Moments:
moment = ?
Back: moment = force × perpendicular distance

Front: CHECK YOURSELF
Masses of 7 kg and 3 kg hang over a smooth pulley. Write the two equations of motion.
Back: 7g − T = 7a for the falling mass, T − 3g = 3a for the rising one; adding gives a = 0.4g.

Front: CHECK YOURSELF
A 5 kg crate is pulled by 30 N against 10 N of resistance. Find its acceleration.
Back: Resultant 20 N, so a = 20/5 = 4 m s⁻²: F = ma uses the resultant, never a single force.

Front: STANDARD RESULT — LEARN IT
The friction law:
F ? μR
Back: F ≤ μR, equality only at the limit or when sliding

Front: STANDARD RESULT — LEARN IT
Weight:
W = ?
Back: W = mg, with g = 9.8 m s^−2