Question bank

A-Level CAIE Physics 12 1 Kinematics Of Uniform Circular Motion Question Bank

Practice A-Level CAIE Physics 12 1 Kinematics Of Uniform Circular Motion questions by syllabus topic with past-paper context, marks, difficulty and question previews on Eduninja.

10 matching questions · Open interactive library

Question 1

1

2 marks

Question 1(a)

1(a)

Define the radian.

Easystructured1 marks

Answer

angle (subtended at the centre of a circle) when arc (length) = radius B1

Question 1(b)

1(b)

A circular metal disc spins horizontally about a vertical axis, as shown in Fig. 1.1. A piece of modelling clay is attached to the disc. For the instant when the piece of modelling clay is in the position shown, draw on Fig. 1.1:

structured1 marks

Question 1(b)(i)

1(b)(i)

an arrow, labelled V , showing the direction of the velocity of the modelling clay

Mediumstructured1 marks

Answer

arrow, labelled V, pointing in NE direction B1

Question 1(c)

1(c)

The metal disc in Fig. 1.1 has a radius of 9.3 cm . The centre of gravity of the modelling clay is 1.2 cm from the rim of the disc and moves with a speed of \(0.68 \mathrm{~ms}^{-1}\).

structured0 marks

Question 1(c)(i)

1(c)(i)

Calculate the angular speed \(\omega\) of the disc. \(\omega=\) \(\mathrm{rads}^{-1}\)

Mediumstructured0 marks

Answer

\(v=r \omega\) C1 \[ \begin{aligned} \omega =0.68 /(0.093-0.012) =8.4 \mathrm{rad} \mathrm{~s}^{-1} \end{aligned} \] A1

Question 1

1

4 marks

Question 1(a)

1(a)

Define the radian.

Easystructured1 marks

Answer

angle (subtended at centre of circle) when arc length = radius B1

Question 1(b)

1(b)

The minute hand of a clock revolves at constant angular speed around the face of the clock, completing one revolution every hour. A small piece of modelling clay is attached to the hand with its centre of gravity at a distance L from the fixed end of the hand, as shown in Fig. 1.1. Calculate the angular speed \(\omega\) of the minute hand.

Mediumstructured0 marks

Answer

\(\omega=2 \pi / T\) C1 \[ \begin{aligned} =2 \pi /(1.0 \times 60 \times 60) =1.7 \times 10^{-3} \mathrm{rad} \mathrm{~s}^{-1} \end{aligned} \] A1

Question 1(c)

1(c)

During a time interval of 1400 s , the centre of gravity of the piece of modelling clay in Fig. 1.1 moves through a total distance of 0.44 m .

structured3 marks

Question 1(c)(i)

1(c)(i)

Calculate the angle through which the minute hand moves in this time interval.

Mediumstructured1 marks

Answer

\[ \begin{aligned} \text { angle } =1.7 \times 10^{-3} \times 1400 =2.4 \mathrm{rad} \end{aligned} \] A1

Question 1(c)(ii)

1(c)(ii)

Determine distance L.

Mediumstructured2 marks

Answer

\[ \begin{aligned} L & =\text { arc length } / \text { angle } & =0.44 / 2.4 \end{aligned} \] or \[ L=0.44 \times(3600 / 1400) / 2 \pi \] C1 \(L=0.18 \mathrm{~m}\) A1

Question 1

1

2 marks

Question 1(d)

1(d)

Another satellite is in a circular orbit around the Earth with the same orbital radius and period as the satellite in (c).

structured2 marks

Question 1(d)(i)

1(d)(i)

Calculate the angular speed of the satellite in this orbit. Give a unit with your answer. angular speed = unit

Easystructured2 marks

Answer

\(\omega=2 \pi / T\) C1 \[ \begin{aligned} =2 \pi /(24 \times 60 \times 60) =7.3 \times 10^{-5} \mathrm{rad} \mathrm{~s}^{-1} \end{aligned} \] A1

Question 1

1

4 marks

Question 1(b)

1(b)

Artemis is a spherical planet that may be assumed to be isolated in space. The variation with distance x from the centre of Artemis of the gravitational potential \(\phi\) is shown in Fig. 1.1.

structured4 marks

Question 1(b)(iv)

1(b)(iv)

A satellite is in an orbit at a fixed position above a point on the surface of Artemis. The satellite is located above the equator of Artemis at a height above the surface where the gravitational potential is \(-0.65 \times 10^{7} \mathrm{Jkg}^{-1}\). Calculate the period, in hours, of rotation of Artemis. period = hours

Hardstructured4 marks

Answer

r in range \(2.60 \times 10^{7}\) to \(2.65 \times 10^{7} \mathrm{~m}\) C1 \(\frac{m v^{2}}{r}=\frac{G M m}{r^{2}}\) and \(v=\frac{2 \pi r}{T}\) or \(m r \omega^{2}=\frac{G M m}{r^{2}}\) and \(\omega=\frac{2 \pi}{T}\) C1 \(T^{2}=\frac{4 \pi^{2} r^{3}}{G M}=\frac{4 \pi^{2} \times\left(2.65 \times 10^{7}\right)^{3}}{6.67 \times 10^{-11} \times 2.55 \times 10^{24}}=4.20 \times 10^{9}\) C1 \[ T=64800 \mathrm{~s} \] \[ \text { = } 18 \text { hours } \] A1

Question 1

1

2 marks

Question 1(a)

1(a)

With reference to velocity and acceleration, describe uniform circular motion.

Mediumstructured2 marks

Answer

constant speed or constant magnitude of velocity B1 acceleration (always) perpendicular to velocity B1

Question 1

1

1 marks

Question 1(b)

1(b)

The Earth and the Moon may be considered to be isolated in space with their masses concentrated at their centres. The orbit of the Moon around the Earth is circular with a radius of \(3.84 \times 10^{5} \mathrm{~km}\). The period of the orbit is 27.3 days. Show that

structured1 marks

Question 1(b)(i)

1(b)(i)

the angular speed of the Moon in its orbit around the Earth is \(2.66 \times 10^{-6} \mathrm{rad} \mathrm{s}^{-1}\),

Easystructured1 marks

Answer

\(\omega=2 \pi /(27.3 \times 24 \times 3600)\) or \(2 \pi /\left(2.36 \times 10^{6}\right) \quad\) M1

Question 1

1

A planet of mass m is in a circular orbit of radius r about the Sun of mass M, as illustrated in Fig. 1.1. The magnitude of the angular velocity and the period of revolution of the planet about the Sun are \(\omega\) and T respectively.

structured5 marks

Question 1(a)

1(a)

State

structured3 marks

Question 1(a)(i)

1(a)(i)

what is meant by angular velocity,

Easystructured2 marks

Answer

rate of change of angle / angular displacement M1 swept out by radius A1

Question 1(a)(ii)

1(a)(ii)

the relation between \(\omega\) and T.

Easystructured1 marks

Answer

\(\omega \times T=2 \pi\)

Question 1(c)

1(c)

Data for the planets Venus and Neptune are given in Fig. 1.2. Assume that the orbits of both planets are circular.

structured2 marks

Question 1(c)(ii)

1(c)(ii)

Determine the linear speed of Venus in its orbit. speed = \(\mathrm{km} \mathrm{s}^{-1}\)

Mediumstructured2 marks

Answer

speed \(=\left(2 \pi \times 1.08 \times 10^{8}\right) /(0.615 \times 365 \times 24 \times 3600) \quad\) C1

Question 1

1

gravitational potential energy, energy = J

structured3 marks

Question 1(a)

1(a)

Define the radian.

Easystructured2 marks

Answer

angle (subtended) at centre of circle B1 (by) arc equal in length to radius B1 [2]

Question 1(b)

1(b)

A stone of weight 3.0 N is fixed, using glue, to one end P of a rigid rod C P, as shown in Fig. 1.1. The rod is rotated about end C so that the stone moves in a vertical circle of radius 85 cm . The angular speed \(\omega\) of the rod and stone is gradually increased from zero until the glue snaps. The glue fixing the stone snaps when the tension in it is 18 N . For the position of the stone at which the glue snaps,

structured4 marks

Question 1(b)(ii)

1(b)(ii)

calculate the angular speed \(\omega\) of the stone. \(\mathrm{rad} \mathrm{s}^{-1}[4]\)

Mediumstructured4 marks

Answer

\((\max )\) force / tension = weight + centripetal force C1 centripetal force \(=m r \omega^{2} \quad\) C1 \(15=3.0 / 9.8 \times 0.85 \times \omega^{2} \quad\) C1 \(\omega=7.6 \mathrm{rad} \mathrm{s}^{-1} \quad\) A1 [4]

Question 2

2

2 marks

Question 2(b)

2(b)

Positronium is a system in which an electron and a positron orbit, with the same period, around their common centre of mass, as shown in Fig. 2.1. The radius r of the orbit of both particles is \(1.59 \times 10^{-10} \mathrm{~m}\).

structured2 marks

Question 2(b)(iii)

2(b)(iii)

Use the information in (b)(ii) to determine the period of the circular orbit of the two particles.

Mediumstructured2 marks

Answer

\[ \begin{aligned} F=m r \omega^{2} \text { and } \_\omega=2 \pi / T \text { or } F=m v^{2} / r \text { and } v=2 \pi r / T \end{aligned} \] C1 \[ \begin{aligned} F=4 \pi^{2} m r / T^{2} T=\sqrt{ }\left[4 \pi^{2} \times 9.11 \times 10^{-31} \times 1.59 \times 10^{-10} /\left(2.28 \times 10^{-9}\right)\right] \end{aligned} \] \(=1.58 \times 10^{-15} \mathrm{~s}\) C1 A1

Question 2

2

A steel sphere of mass 0.29 kg is suspended in equilibrium from a vertical spring. The centre of the sphere is 8.5 cm from the top of the spring, as shown in Fig. 2.1. The sphere is now set in motion so that it is moving in a horizontal circle at constant speed, as shown in Fig. 2.2. The distance from the centre of the sphere to the top of the spring is now 10.8 cm .

structured3 marks

Question 2(b)

2(b)

The angle between the linear axis of the spring and the vertical is \(27^{\circ}\).

structured1 marks

Question 2(b)(i)

2(b)(i)

Show that the radius r of the circle is 4.9 cm .

Mediumstructured1 marks

Answer

\(r=10.8 \times \sin 27^{\circ}=4.9 \mathrm{~cm}\) A1

Question 2(c)

2(c)

2 marks

Question 2(c)(ii)

2(c)(ii)

Calculate the period of the circular motion of the sphere.

Mediumstructured2 marks

Answer

\[ a=r \omega^{2} \text { and } \omega=2 \pi / T \] or \[ a=v^{2} / r \text { and } v=2 \pi r / T \] C1 \[ \begin{aligned} T =2 \pi \times \sqrt{ }(0.049 / 5.0) =0.62 \mathrm{~s} \end{aligned} \] A1