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AS 91524 · 2025 paper · momentum & circular motion

Question 1(a) Achieved

Practises Linear momentum & collisions

Titan is the largest of Saturn's moons. Ignore every other body, and assume Titan is in a perfectly circular orbit.

M Saturn5.68×10²⁶ kg
r Saturn5.82×10⁷ m
M Titan1.35×10²³ kg
centre-to-centre1.22×10⁹ m

Show (Saturn + Titan) has its centre of mass 2.90×10⁵ m from Saturn's centre.

The 2025 paper, page 2 ↗ Marking schedule, page 1 ↗

Work it out

Try it on paper first. Stuck? Take one hint at a time.

  1. 1 How do you find the centre of mass of two bodies along the line joining them?

    Measure every position from Saturn’s centre, so Saturn is at x = 0 and Titan at x = 1.22 × 10⁹ m. Then xCOM = (mSxS + mTxT) / (mS + mT).

  2. 2 Put the values in. It is a “show that”, so keep every digit of the result.

    xCOM = (5.68 × 10²⁶ × 0 + 1.35 × 10²³ × 1.22 × 10⁹) / (5.68 × 10²⁶ + 1.35 × 10²³) = 1.647 × 10³² / 5.681 35 × 10²⁶ = 289 896 m

  3. 3 Does that agree with the value in the question? And does the size make sense?

    289 896 m is 2.90 × 10⁵ m to three figures. It is far smaller than Saturn’s radius (5.82 × 10⁷ m), so the pair’s centre of mass lies deep inside Saturn, as it should for a moon over 4000 times lighter than its planet.
Answer 289 896 m (2.899 × 10⁵ m) from Saturn’s centre, which rounds to the 2.90 × 10⁵ m asked for.

What the marker wanted

  • Achieved The equation with the values put in, or the equation and the unrounded result.

In our words, from NZQA’s 2025 marking schedule.

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Common mistake

Writing 2.90 × 10⁵ m as your answer. The question has told you that already, so the mark is for the equation with the numbers in and the unrounded result. NZQA’s 2025 report says candidates who did not reach Achieved often skipped the starting equation and the algebra in “show” questions.

How did it go?

Got it moves it further out. Review brings it back tomorrow.