Circular motion: past paper questions

Where the questions come from

• Question 2May/June 2026, paper 31Structured5 marksHas a diagram

  The point $B$ is vertically below the point $A$. One end of a light inextensible string is attached to $A$, and the other end is attached to $B$. A particle $P$ of mass $7\text{ kg}$ is attached to the string so that the length $AP$ is $15\text{ m}$.

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• Question 2Oct/Nov 2025, paper 31Structured4 marks

  A particle $P$ of mass $m$ is moving in a horizontal circle with angular speed ${\omega }_1$ on the smooth inner surface of a hemispherical shell of radius $r$.

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• Question 2Oct/Nov 2024, paper 31Structured5 marks

  A particle $P$ of mass $m$ is attached to one end of a light inextensible string of length $a$. The other end of the string is attached to a fixed point $O$. The particle $P$ is held at the point $A$ with the string taut.

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• Question 5May/June 2026, paper 31Structured9 marks

  A particle of mass $m$ is attached to a fixed point $O$ by a light inextensible string of length $a$. The particle initially hangs directly below $O$ at the point $A$. The particle is then projected horizontally with speed $2\sqrt{ag}$, and begins to move in a vertical circle.

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• Question 6Oct/Nov 2025, paper 31Structured8 marksHas a diagram

  A particle $P$ of mass $m$ is attached to one end of a light inextensible string of length $a$. The other end of the string is attached to a fixed point $O$. Initially $P$ is held with the string taut and making an angle of ${60}^{\circ }$ with the upward vertical through $O$.

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• Question 6Oct/Nov 2024, paper 31Structured8 marksHas a diagram

  A particle $P$ of mass $0.05\mathrm{k}\mathrm{g}$ is attached to one end of a light inextensible string of length $1\mathrm{m}$. The other end of the string is attached to a fixed point $O$.

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• Question 1Oct/Nov 2025, paper 32Structured4 marksHas a diagram

  A particle $P$ of mass $m$ is attached to two light inextensible strings each of length $l$. The end of one string is attached to a fixed point $A$ and the end of the other string is attached to a fixed point $B$, with $A$ vertically above $B$. Angle $APB$ is a right angle.

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• Question 1Oct/Nov 2024, paper 32Structured3 marks

  A particle of mass $2\text{ kg}$ is attached to one end of a light elastic string of natural length $0.8\text{ m}$ and modulus of elasticity $100\text{ N}$. The other end of the string is attached to a fixed point $O$ on a smooth horizontal surface.

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• Question 6Oct/Nov 2025, paper 32Structured8 marksHas a diagram

  A fixed smooth sphere with radius $a$ and centre $O$ rests on horizontal ground. A particle is projected horizontally from the highest point, $A$, of the sphere with speed $u$. The particle begins to move in a vertical circle along the surface of the sphere.

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• Question 5May/June 2023, paper 31Structured7 marks

  A light elastic string of natural length $a$ and modulus of elasticity $\lambda mg$ has one end attached to a fixed point $O$ on a smooth horizontal surface.

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• Question 1May/June 2026, paper 33Structured5 marks

  A particle $P$ of mass $m$ is moving in a horizontal circle with constant angular speed $\omega$ on the smooth inner surface of a hemispherical shell of radius $a$. The plane of the circular motion is at a height $h=\frac{1}{3}a$ above the lowest point on the shell.

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• Question 3May/June 2026, paper 33Structured5 marksHas a diagram

  A fixed smooth solid sphere has centre $O$ and radius $a$.

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• Question 3May/June 2025, paper 31Structured7 marksHas a diagram

  A rough horizontal disc, centre $O$, rotates with constant angular speed $\omega \text{ rad}{\text{s}}^{-1}$.

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• Question 5May/June 2024, paper 31Structured7 marks

  Two particles $A$ and $B$ of masses $m$ and $km$ respectively are connected by a light inextensible string of length $a$. The particles are placed on a rough horizontal circular turntable with the string taut and lying along a radius of the turntable.

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• Question 7May/June 2025, paper 31Structured10 marksHas a diagram

  A fixed hollow sphere has radius $a$ and centre $O$. The points $A$, $B$ and $C$ lie on the inner surface of the sphere with $OA$ and $BC$ horizontal.

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• Question 7May/June 2024, paper 31Structured9 marks

  A smooth sphere with centre $O$ and of radius $a$ is fixed to a horizontal plane. A particle $P$ of mass $m$ is projected horizontally from the highest point of the sphere with speed $u$, so that it begins to move along the surface of the sphere.

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• Question 5May/June 2025, paper 33Structured8 marksHas a diagram

  A hollow cylinder of radius $r$ is fixed with its axis horizontal. Points $A$, $B$ and $O$ are in the same vertical plane perpendicular to the axis of the cylinder, with $A$ and $B$ on the smooth inner surface and $O$ on the axis.

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• Question 3May/June 2024, paper 33Structured7 marks

  A particle $P$ of mass $m$ is attached to one end of a light inextensible string of length $a$. The other end of the string is attached to a fixed point $O$.

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