Mechanics of a wheel falling off the edge of a table. Continue reading
III/2007/9 – Two small beads, A and B, each of mass m, are threaded on a smooth horizontal circular hoop of radius a and centre O. The angle θ is the acute angle determined by 2 θ = AOB.
The beads are connected by a light straight spring. The energy stored in the spring is
where k and α are constants satisfying k > 0 and
The spring is held in compression with θ = β and then released. Find the period of oscillations in the two cases that arise according to the value of θ and state the value of β for which oscillations do not occur. Continue reading
I/1999/2 – A point moves in the x,y plane so that the sum of the squares of its distances from the three fixed points is always .
Find the equation of the locus of the point and interpret it geometrically.
Explain why cannot be less than the sum of the squares of the distances of the three points from their centroid. Continue reading