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Date	November 2020	Marks available	2	Reference code	20N.3.SL.TZ0.6
Level	Standard level	Paper	Paper 3	Time zone	0 - no time zone
Command term	Show that	Question number	6	Adapted from	N/A

Question

A bar rotates horizontally about its centre, reaching a maximum angular velocity in six complete rotations from rest. The bar has a constant angular acceleration of $0.110 rad s^{- 2}$ . The moment of inertia of the bar about the axis of rotation is $0.0216 kg m^{2}$ .

Show that the final angular velocity of the bar is about $3 rad s^{- 1}$ .

[2]

a.

Draw the variation with time $t$ of the angular displacement $θ$ of the bar during the acceleration.

[1]

b.

Calculate the torque acting on the bar while it is accelerating.

[1]

c.

The torque is removed. The bar comes to rest in $30$ complete rotations with constant angular deceleration. Determine the time taken for the bar to come to rest.

[2]

d.

Markscheme

${ω_{f}}^{2} = 0 + 2 \times 0.110 \times 6 \times 2 π$ ✓

$ω_{f} = 2.88 « rad s^{- 1} »$ ✓

Other methods are possible.
Answer 3 given so look for correct working
At least 2 sig figs for MP2.

a.

concave up from origin ✓

b.

$Γ = « I α so Γ = 0.110 \times 0.0216 = » 2.38 \times 10^{- 3} « N m »$ ✓

c.

$α = \frac{2 . 9^{2}}{2 \times 2 π \times 30} =$ OR $- 0.022 « rad s^{- 2} »$ ✓

$t « = \frac{ω_{f} - ω_{i}}{α} = \frac{- 2.9}{- 0.0220} » = 130 « s »$ ✓

Other methods are possible.

Allow $131 s$ if $2.88$ used

Allow $126 s$ if $3$ used

Award [2] marks for a bald correct answer

d.

Examiners report

[N/A]

a.

[N/A]

b.

[N/A]

c.

[N/A]

d.

Syllabus sections

Option B: Engineering physics » Option B: Engineering physics (Core topics) » B.1 – Rigid bodies and rotational dynamics

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20N.3.SL.TZ0.8:
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Option B: Engineering physics