Physics - New Zealand Scholarship Physics
Scholarship Physics rewards the quality of your reasoning far more than the number of formulae you can recall. Questions typically ask you to derive a relationship, justify an approximation, or analyse experimental data, and then use that result in a later part of the same question.
Core rules and concepts
- Define every symbol and show each algebraic step. An unexplained jump loses the reasoning credit even when the final answer is correct.
- Justify approximations explicitly: state the condition (for example θ ≪ 1, so sin θ ≈ θ) and check it numerically before you rely on the simplified result.
- Linearise before plotting - ln y against ln x for a power law, y against 1/x for an inverse relation - and read the exponent or constant from the gradient.
- Check dimensions and limiting cases: send a parameter to zero or infinity and confirm the expression still behaves physically.
- Expect synoptic questions: one part may need energy conservation, Newton's second law applied to circular motion, and an uncertainty estimate.
Worked example
A block slides from rest down a frictionless track into a vertical circular loop of radius r. Find the minimum release height h above the bottom of the loop for the block to stay in contact.
At the top, 'just losing contact' means the normal force is zero, so gravity alone supplies the centripetal force: mg = mv²/r, giving v² = gr. Conservation of energy from release to the top gives:
mgh = mg(2r) + ½mv² = 2mgr + 0.5mgr,
so h = 2.5r. The check: h must exceed 2r, and the surplus 0.5r is the kinetic energy the block must still carry at the top.
Traps that cost marks
- Setting v = 0 at the top. A block arriving with no speed has already left the track; the correct condition is N = 0.
- Reading 'slides' as 'rolls'. For a rolling sphere the rotational kinetic energy raises the answer to 2.7r.
- Stating an answer without the inequality h > 2r or a limiting-case check.