IB Physics HL A.2.23 Circular Motion

Practise analysing HL circular-motion systems, including banked paths, orbital acceleration and rotational data.

Exam points

calculate centripetal acceleration using v²/r, ω²r or 4π²r/T²
identify the radial direction of centripetal acceleration toward the centre of circular motion
relate angular speed, period, radius and linear speed in uniform circular motion

[Maximum number: 7]

Aibhe and Euan are sitting on opposite sides of a merry-go-round, which is rotating at constant speed around a fixed centre. The diagram below shows the view from above.

Figure for Question A.2.23—Centripetal acceleration question 1 — IB Physics HL

Aibhe is moving at speed $1.0 \mathrm{~m} \mathrm{~s}^{-1}$ relative to the ground.

(a)

Determine the magnitude of the velocity of Aibhe relative to

[ 2 ]

(i)

Euan.

[ 1 ]

2.0 or $0\left(\mathrm{~ms}^{-1}\right)$ ;

(ii)

the centre of the merry-go-round.

[ 1 ]

1.0 or $0\left(\mathrm{~ms}^{-1}\right)$ ;

(b)

Outline why Aibhe is accelerating even though she is moving at constant speed.

[ 2 ]

(c)

Draw an arrow on the diagram on page 29 to show the direction in which Aibhe is accelerating.

[ 1 ]

(d)

Aibhe moves so that she is sitting at a distance of 0.75 m from the centre of the merry-go-round, as shown below.

Euan pushes the merry-go-round so that he is again moving at $1.0 \mathrm{~ms}^{-1}$ relative to the ground.

[ 2 ]

(i)

Calculate the magnitude of Aibhe's acceleration.
Part 2 Charge-coupled devices (CCDs)

[ 2 ]

$\quad a\left(=\frac{v^{2}}{r}\right)=\frac{0.5^{2}}{0.75}$ ;
$a=0.33\left(\mathrm{~ms}^{-2}\right)$ ;

Marking guidance:

Allow ECF from (d)(i).
Award [2] for a bald correct answer.

Part 2 Charge-coupled devices (CCDs)

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A.2.23—Centripetal acceleration question 1

Question (a)

Question (i)

Question (ii)

Question (b)

Question (c)

Question (d)

Question (i)