(a) A woman at the equator weights herself daily on a bathroom
scale. Suppose that the earth rotates 3x faster, will the reading
change?
Yes, it will change. If the Earth rotates faster, it means that
the woman requires more centripetal force. Bathroom scales measure
the reaction force. If we draw the free body diagram of the woman,
mg - R = resultant force = mv^2/r
Hence, R = mg - mv^2/r .
If it rotates 3 times as fast, mv^2/r will be larger, and hence
R will be smaller.
(b) The moon does not fall towards the earth although it is
udner the pull of earth's gravity.
The Earth's gravitational force is used for accelerating towards
the Earth's centre constantly, resulting in a circular orbit by the
Moon.
(a) A car going over a hump (a circular arc) - It should be
minimum speed but dont know how to explain...
Requires maximum speed. You don't see cars travelling slowly
being unable to clear a hump right?
Too fast a speed, you will need a larger centripetal force. If
the weight of the car is insufficient to supply the required
centripetal force, the car will fly and lose contact with the
hump
(b) water in a pail being swung in a verrtical circle (hmmm,
minimum speed at the top and max speed at the bottom?)
No, you need a minimum speed at the bottom and top of the
circle.
If the speed is too slow, at the top of the circular motion, the
water will fall out of the pail.
If fast enough, the pail will exert a force on the water for the
circular motion, and by N3L, the water will exert an equal but
opposite force on the pail, and hence it won't fall out.
(c) A bus negotiating a circular bend on the road (not very sure
about this one.)
Maximum speed required.
If too fast, it might topple. Think of the times you took a
bus.