Title: InkPhysics / Engineering physics
On every note of this deck, unless a note says otherwise:
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Front: DEFINITION
Define: Adiabatic change.
Back: A change with no heat entering or leaving: Q = 0, pV^γ = constant, and ΔU = −W.

Front: RECALL
Explain why a skater speeds up as she pulls her arms in.
Back: Her mass moves towards the axis, so I falls; with no external torque Iω is fixed, so ω rises. Her muscles do work pulling inward, so the kinetic energy rises as well.

Front: DEFINITION
Define: Isothermal change.
Back: A change at constant temperature: pV = constant and ΔU = 0, so Q = W.

Front: SPOT THE ERROR
Say what is wrong with this claim: How hard something is to set spinning depends only on its mass.
Back: Mass alone does not decide it. The moment of inertia sums mr^2, so where the mass sits counts squared: a light hoop with everything at the rim can resist spin-up more than a heavier disc whose mass hugs the axis.

Front: DEFINITION
Define: Angular velocity.
Back: The rate of change of angular displacement: ω = Δθ/Δt, measured in rad s^−1.

Front: RECALL
State how the distribution of mass changes the moment of inertia.
Back: Mass concentrated far from the axis gives a large I and mass hugging the axis a small one, because every contribution counts the distance squared.

Front: RECALL
State the first law of thermodynamics.
Back: Q = ΔU + W, where Q is the heat supplied to the gas, ΔU the increase in its internal energy and W the work done by the gas.

Front: SPOT THE ERROR
Say what is wrong with this claim: Heating a gas always makes it hotter.
Back: Heat raises the temperature only if it stays as internal energy. In an isothermal expansion ΔU = 0, so Q = W: every joule supplied leaves again as work and the temperature never moves.

Front: RECALL
State the maximum theoretical efficiency of a heat engine.
Back: (T_H − T_C)/T_H, with both temperatures in kelvin.

Front: SPOT THE ERROR
Say what is wrong with this claim: A skater pulling in her arms spins faster because her muscles give her an extra twist.
Back: No extra twist is added, and none could be: internal forces cannot change angular momentum. Pulling her arms in cuts I, and because Iω is conserved ω must rise. Her muscles supply work, which is why the kinetic energy rises, not momentum.

Front: RECALL
State the efficiency of a heat engine.
Back: efficiency = W/Q_H = (Q_H − Q_C)/Q_H.

Front: RECALL
State how work done is found from a p-V diagram.
Back: It is the area under the curve between the two volumes; at constant pressure that area is the rectangle pΔV.

Front: DEFINITION
Define: Moment of inertia.
Back: The sum of mr^2 taken over every particle of a body: its resistance to angular acceleration about that axis, in kg m^2.

Front: DEFINITION
Define: Angular momentum.
Back: The product of moment of inertia and angular velocity, Iω, in kg m^2 s^−1.

Front: EQUATION · NOT ON THE DATA SHEET
Acceleration along the arc at radius r:
a = ?\(a = \, ?\)a = ?
Back: a = αr\(a = \alpha r\)a = αr

Front: DEFINITION
Define: Indicated power.
Back: The power developed by the gas inside the cylinders: the area of the p-V loop × cycles per second × the number of cylinders.

Front: SPOT THE ERROR
Say what is wrong with this claim: A perfect engine would turn all the fuel's heat into useful work.
Back: Even a perfect engine must dump heat. The working substance has to be returned to its starting state each cycle, so heat Q_C is rejected to a colder sink and the efficiency is capped at (T_H − T_C)/T_H, below 1 for any real pair of temperatures.

Front: RECALL
Explain why no heat engine can be 100% efficient.
Back: The working substance must be returned to its starting state to repeat the cycle, which means rejecting heat Q_C to a colder sink, so W is always less than Q_H.

Front: RECALL
Explain why a flywheel carries its mass at the rim.
Back: r^2 rewards distance, so rim mass maximises I and with it the energy ½Iω^2 stored at a given spin rate.

Front: DEFINITION
Define: Torque.
Back: The turning effect of a force about an axis: T = Fr for a force applied tangentially at radius r, in N m.

Front: RECALL
State the principle of conservation of angular momentum.
Back: With no external torque acting, the total angular momentum Iω of a system stays constant.