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AL-Essay-Circular motion / p.1
1.
(90-IIA-6)
(a) Derive an expression for the force experienced by an object of mass m which is rotating with
angular velocity w around a circular path of radius r, in the absence of any gravitational field.
(4 marks)
(b) In a laboratory a small weight is attached by a piece of string of length l to a fixed point and set
into circular motion in a horizontal plane. Derive an expression for the angle of inclination of the
string with the vertical, explaining what happens as w is increased to a high value.
(3 marks)
(c) A closed tube containing a mixture of two liquids of densities  and   (  >   ) is attached at
the end by a hinge (allowing vertical motion) to a rigid rod. If this rod, and also the tube, is
rapidly rotated in a horizontal plane with an angular velocity w, compare the excess forces on a
small elemental volume A r of each liquid at distance r from the centre of motion (A being the
area of cross-section of the tube). Hence explain the action of a centrifuge.
(d)
(5 marks)
A student argues that there is no need to use a centrifuge to separate the two liquids since if the
mixture is just left stationary they will separate under the force of gravity. Compare the excess
forces using each method and comment on the statement of the student.
(4 marks)
2.
(94-IIB-1a)
(a) The figure shows a car travelling over a hump which is an arc of a vertical circle. Compared with
travelling on a level road, would a passenger feel heavier, lighter or the same as usual when the
car passes the top of the hump? Briefly explain your answer. (Assume that the passenger remains
in contact with the seat)
(3 marks)
3.
(96-IIB-1a,b,c)
(a)The centripetal acceleration, a, of a body undergoing a uniform circular motion of radius r can be
expressed as either (1)
(b)
a
v2
2
or (2) a   r , where v and  are linear and angular speeds of
r
the body respectively. For a uniform circular motion of constant period, student A thinks that a
decreases with r according to equation (1), while student B argues that a increases with r
according to equation (2). Comment on their arguments.
(2 marks)
To study a circular motion, a small rubber bung of mass m is attached to one end of a piece of
string passing through a thin glass tube, which has a weight W hanging at its other end. The
rubber bung is set into a horizontal circular motion by a student holding the glass tube.
(i)
Draw a diagram to show the forces acting on the rubber bung and explain why the string is
not horizontal but dips at a small angle  .
AL-Essay-Circular motion / p.2
Show that the weight W equals m L in theory, where  is the angular speed and L is the
length of the string beyond the upper opening of the glass tube. Give TWO reasons to
explain why there are discrepancies between the experimental and theoretical results.
(iii) Suggest TWO ways to increase the rate of revolution of the rubber bung.
(iv) When the rubber bung is at position A, the string suddenly breaks. Describe and explain its
subsequent motion.
(7 marks)
With the aid of a diagram, describe and explain the action of a centrifuge. Give a practical use of a
centrifuge.
(5 marks)
2
(ii)
(c)
4.
(04-IIB-1a)
(a)(i)
The figure shows a particle moving with uniform speed v in horizontal circle of
radius r.
With the aid of a vector diagram, find an expression for the change in velocity v as the
particle moves from, say, point A to an adjacent point B in time t. Hence, determine the
magnitude and direction of its acceleration at point A.
(ii)
A pendulum bob is attached to a string
and made to revolve in a horizontal
circle as shown. If the length of the
string is L, derive the relation between
the period of motion and the angle that
the spring makes with the vertical.
(Neglect air resistance.)
(iii)
With the aid of a diagram, explain why
a person on a bicycle has to lean
inwards when riding round a horizontal
circular track.
(10 marks)