Questions
Q5.7 The ball would not behave as it would when dropped on the Earth. As the astronaut holds the ball,
she and the ball are moving with the same angular velocity. The ball, however, being closer to the
center of rotation, is moving with a slower tangential velocity. Once the ball is released, it acts
according to Newton's first law, and simply drifts with constant velocity in the original direction of its
velocity when released — it is no longer "attached" to the rotating space station. Since the ball follows
a straight line and the astronaut follows a circular path, it will appear to the astronaut that the ball will
"fall to the floor". But other dramatic effects will occur. Imagine that the ball is held so high that it is
just slightly away from the center of rotation. Then, as the ball is released, it will move very slowly
along a straight line. Thus, the astronaut may make several full rotations around the circular path
before the ball strikes the floor. This will result in three obvious variations with the Earth drop. First,
the time to fall will be much larger than that on the Earth, even though the feet of the astronaut are
pressed into the floor with a force that suggests the same force of gravity as on Earth. Second, the ball
may actually appear to bob up and down if several rotations are made while it "falls". As the ball
moves in a straight line while the astronaut rotates, sometimes she is on the side of the circle on which
the ball is moving toward her and other times she is on the other side, where the ball is moving away
from her. The third effect is that the ball will not drop straight down to her feet. In the extreme case
we have been imagining, it may actually strike the surface while she is on the opposite side, so it looks
like it ended up "falling up". In the less extreme case, in which only a portion of a rotation is made
before the ball strikes the surface, the ball will appear to move backward relative to the astronaut as it
falls.
Q5.8 Inertial reaction. The water tends to move along a straight line, but the bucket pulls it in and around in
a circle.
Q5.11. The speed changes. The tangential force component causes tangential acceleration.
Q5.13 Face area and drag coefficient change when a skydiver opens a parachute.
Problems
Chapter 6
Questions
Q6.2 The force is perpendicular to every increment of displacement. Therefore, F ⋅∆r = 0.
Q6.3 Yes. Force times distance over which the toe is in contact with the ball. No. Yes. Air friction and
gravity.
Q6.6 (a) Tension (b) Air resistance
(c) Positive in increasing velocity on the downswing. Negative in decreasing velocity on the
upswing.
Problems
