Aptitude Test Problems in Physics Science for Everyone by S Krotov ( PDFDrive.com )

126 Aptitude Test Problems in Physics

(OA = R) such that points 0, S, A, and J lie on
the same straight line. Then it is clear that ON =
R + r at any instant of time. Besides, point 0 is at
rest relative to John (Sam is always opposite to
John). Therefore, from John's point of view, Nick
translates in a circle of radius R + r with the cen-
tre at point 0 which moves relative to the ground
in a circle of radius R with the centre at point A.
From Nick's point of view, Sam translates in a
circle of radius R + r with the centre at point 0
which is at rest relative to Nick. However, point 0
moves relative to the ground in a circle of radius r
with the centre at point B.
1.24. Since the hoop with the centre at point 0 1
is at rest, the velocity vA of the upper point A of
"intersection" of the hoops must be directed along
the tangent to the circle with centre 0 1 at any in-

Fig. 140

stant of time (Fig. 140). At any instant of time,

the segment AB divides the distance d = 00^1 be-

tween the centres of the hoops into two equal parts,

and hence the horizontal projection of the velocity

vA is always equal to v/2. Consequently, the ve-

locity vA forms an angle q = n/2 — a with the

horizontal and is given by

v v

.....

vA— 2 cos cp 2 sin a