From Chapter 5
8.8.A wheel is rotating at a rate of 2.0 revolutions every 3.0 s. Through what angle, in
radians, does the wheel rotate in 1.0 s?
=
t, with
in radians,
in radians/s and
t in seconds
2.0 revolutions in radians will be 2x2
p
radians accomplished in 3 s, so
will be
The angle of rotation in 1 second
2x2
p
/3.0s = 4
p
/3.0s =4.19 rd
12.14.
.The rotor in an amusement park ride where people stand against the inside of a
cylinder. Once the cylinder is spinning fast enough, the floor drops out. (a) What force
keeps the people from falling out the bottom of the cylinder? (b) If the coefficient of
friction is 0.40 and the cylinder has a radius of 2.5 m, what is the minimum angular speed
of the cylinder so that
the people don’t fall out? (Normally the operator runs it
considerably faster as a safety measure.)
a)
the force of static friction
b)
using Newton’s law SF
r
=N = ma
r
= m v
2
/r = m
2
r
but
fs= mg
= μN=μma
r
=μ m
2
r = mg
=v(g/μr)=v(9.8m/s
2
/(0.40*2.5m) =3.1 rad/s
14.16.(*)Earth’s orbit around the Sun is nearly circular. The period is 1 yr = 365.25 days.
(a) In an elapsed time of 1 day, what is Earth’s an
gular displacement? (b) What is the
change in Earth’s velocity,
v
r
? (c) What is Earth’s average acceleration during 1
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 Spring '09
 HUANG
 Mass, Velocity, Felipe, 1 day

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