Angular speed and radial accelerationEdexcel International A Level Further Maths: Subtopic test

1. 1
   A particle moves in a horizontal circle of radius $0.8$ m with constant speed, completing $30$ revolutions per minute.

   (a)

   Find the angular speed of the particle.

   [1 mark]

   • A$\pi$ rad s$^{-1}$
   • B$30$ rad s$^{-1}$
   • C$60\pi$ rad s$^{-1}$
   • D$\frac{\pi}{2}$ rad s$^{-1}$

   (b)

   Find the speed of the particle.

   [1 mark]

   • A$\frac{\pi}{0.8}$ m s$^{-1}$
   • B$0.8\pi^2$ m s$^{-1}$
   • C$1.6\pi$ m s$^{-1}$
   • D$0.8\pi$ m s$^{-1}$

   (c)

   Find the magnitude and direction of the acceleration of the particle.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A particle $P$ of mass $0.4$ kg is attached to one end of a light inextensible string of length $0.5$ m. The other end of the string is fixed to a point $O$ on a smooth horizontal table, and $P$ moves on the table in a circle with centre $O$ at a constant speed of $3$ m s$^{-1}$.

   (a)

   Find the magnitude of the acceleration of $P$.

   [1 mark]

   • A$6$ m s$^{-2}$
   • B$18$ m s$^{-2}$
   • C$4.5$ m s$^{-2}$
   • D$7.2$ m s$^{-2}$

   (b)

   Find the tension in the string.

   [1 mark]

   • A$18$ N
   • B$1.8$ N
   • C$7.2$ N
   • D$1.2$ N

   (c)

   Find the angular speed of $P$ and the time taken for $P$ to complete one revolution.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A stone of mass $0.2$ kg is attached to one end of a light inextensible string of length $0.6$ m. The other end of the string is fixed to a point $O$ on a smooth horizontal table, and the stone moves in a horizontal circle on the table with centre $O$. The string will break if the tension exceeds $30$ N.

   (a)

   Find the greatest angular speed at which the stone can move without the string breaking.

   [3 marks]

   (b)

   Find the greatest speed of the stone, and the time for one revolution at this speed.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   Two particles $A$ and $B$, of masses $0.3$ kg and $0.2$ kg, are joined by a light inextensible string $AB$. A second light inextensible string joins $A$ to a fixed point $O$ on a smooth horizontal table. The particles move on the table in horizontal circles with centre $O$ at constant angular speed $5$ rad s$^{-1}$, with $O$, $A$ and $B$ always in a straight line, $OA=0.4$ m and $AB=0.5$ m.

   (a)

   (i) Find the speed of each particle.
   (ii) Find the tension in each string.

   [6 marks]

   (b)

   Each string will break if its tension exceeds $12$ N. The angular speed is slowly increased from $5$ rad s$^{-1}$. Show that $OA$ breaks first, and find the angular speed at which this happens.

   [6 marks]

   Total for question 4: 12 marks

End of questions