Angular speed and radial accelerationEdexcel International A Level Further Maths: Mind map

Exam questions on Angular speed and radial acceleration

1. A particle moves in a horizontal circle of radius $0.8$ m with constant speed, completing $30$ revolutions per minute.
   Find the magnitude and direction of the acceleration of the particle.2 marks
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$^{-1}$.
   Find the angular speed of $P$ and the time taken for $P$ to complete one revolution.2 marks
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.
   Find the greatest angular speed at which the stone can move without the string breaking.3 marks