AS 91524 · 2025 paper · rotational motion
Question 2(b) Merit
Practises Rotational dynamics
Rīhari and Jane are on a playground roundabout of radius 1.30 m. Rīhari stands on it while Jane pushes; from rest she steadily accelerates it so it takes 12.0 s to make 4.00 rotations.
| r | 1.30 m |
|---|---|
| 4.00 rotations in 12.0 s | |
| I (roundabout + Rīhari) | 430 kg m² |
Rīhari then drags his foot along the ground, bringing the roundabout to a stop over 19.2 s.
Calculate the average torque that slows it, if the roundabout and Rīhari have a rotational inertia of 430 kg m².
Work it out
Try it on paper first. Stuck? Take one hint at a time.
-
1 How quickly does the roundabout lose its angular velocity?
From 4.1888 rad s⁻¹ to 0 in 19.2 s: α = (ω − ω0) / t = (0 − 4.1888) / 19.2 = −0.218 17 rad s⁻². -
2 Which equation turns an angular acceleration into a torque?
τ = Iα = 430 × (−0.218 17) = −93.81 N m. -
3 What does the minus sign tell you?
That the torque acts against the rotation. It is what slows the roundabout down.
What the marker wanted
- Achieved One of: the angular acceleration (−0.218 rad s⁻²), or τ = Iα used correctly on a wrong angular acceleration.
- Merit The right torque.
In our words, from NZQA’s 2025 marking schedule.
How did it go?
Got it moves it further out. Review brings it back tomorrow.