Announcements
1. HW8 due March 17 (after spring break).
2. Week of March 16 and 18 (after spring break)
Prof. Detweiler will give lectures
Profs. Chan and Hirschfeld will not hold office
hours during that week
Last time: rotational motion
angle
angular velocity
angular acceleration
s

r


t


t
measured in rad
“”
in rad/s
“”
in rad/s2
Angular velocity is a vector
magnitude
Vt  R
Vt

R
directions of tangential velocity vt and angular frequency

vt

vt

vt
Right Hand Rule


out of screen
Example: horizontal circle (from HW!)
A 0.5 kg ball that is tied to the end
of a 1.5-m light cord is revolved in
a horizontal plane, with the cord making
a 30 deg angle with the vertical.
a) Determine the ball’s speed
b) Now the ball is revolved so
that it’s speed is 4.0 m/s. What
angle does the cord make with
the vertical?
Nonuniform circular motion
• The tangential component

of the acceleration at is due
to changing speed
• The centripetal component

of the acceleration ac is due
to changing direction
• Total acceleration can be
found from these
components
a  a a
2
t
2
C

ac

at

a
Don’t confuse:
at   r
2
v
2
ac    r
r
Vertical Circle
• Look at the forces at
the top of the circle
• The minimum speed at
the top of the circle
can be found
vtop  gR
…i.e., the minimum speed to just stay on the track
7.75 In a popular amusement park ride,
a rotating cylinder of radius 3.00 m is
set in rotation at an angular speed of
5.00 rad/s. The floor then drops away,
leaving the riders suspended against the
wall in a vertical position. What
minimum coefficient of friction
between a rider’s clothing and the wall
is needed to keep the rider from
slipping?
7.27 An air puck of mass 0.25 kg is tied to a string and
allowed to revolve in a circle of radius 1.0 m on a
frictionless horizontal table. The other end of the string
passes through a hole in the center of the table, and a mass
of 1.0 kg is tied to it. The suspended mass remains in
equilibrium while the puck on the tabletop revolves. (a)
What is the tension in the string? (b) What is the horizontal
force acting on the puck? (c) What is the speed of the puck?