DP Physics (last assessment 2024)

Question 20N.3.SL.TZ0.6

Date	November 2020	Marks available	[Maximum mark: 6]	Reference code	20N.3.SL.TZ0.6
Level	SL	Paper	3	Time zone	TZ0
Command term	Calculate, Determine, Draw, Show that	Question number	6	Adapted from	N/A

[Maximum mark: 6]

20N.3.SL.TZ0.6

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 $0.0216 kg m^{2}$ .

(a)

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

[2]

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.

(b)

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

[1]

Markscheme

concave up from origin ✓

(c)

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

[1]

Markscheme

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

(d)

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]

Markscheme

$α = \frac{2 . 9^{2}}{2 \times 2 π \times 30} =$ 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

Syllabus sections

Option B: Engineering physics

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

Option B: Engineering physics » Option B: Engineering physics (Core topics)

Question 20N.3.SL.TZ0.6

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