Download Uniform Circular Motion (UCM)

Uniform Circular Motion (UCM)
same
along a
circular path
Uniform Circular Motion -- motion
around a circular path at a constant speed.
1
Conditions describing UCM:
v
• speed = const. (by
definition)
• v ≠ const. (since direction
is changing)
⇒
a≠o
Fnet ≠ 0
2
During UCM the sum of all the
forces acting on the object (Fnet) ≠ 0
and the object is accelerating.
3
In case of UCM the vectors for
acceleration and force point toward
the center.
v
4
Centripetal Force -- any force
that makes an object move in
UCM.
Examples:
1. As the car curves a turn, a passenger is
thrown against the window. What is the force
making the passenger's trajectory curve?
5
2. An object attached to a rope and moving in
a circular path (see picture)
3. A car moving in a circular path
6
4. Moon orbiting Earth (assuming UCM)
5. An amusement park ride which consists of a large
cylinder on radius R spinning about its vertically
oriented axis of symmetry. When the ride reaching a
specific speed, the floor drops and people remain
"fixed" to the walls of the ride.
7
6. Rollecoaster (* not a true UCM)
8
Formulas Describing UCM
Speed during UCM
r
Radius of the circle r and
time t it takes the car to
complete 1 full circle are
known. This time is called a
period of rotation (T)
Find speed.
9
In the reference table find the formula for
centripetal acceleration
ac = v2/r
where
ac -- centripetal acceleration
v -- speed
r -- radius
10
In the reference table find the formula for
centripetal force
Fc = mac
where
Fc -- centripetal force
m -- mass
ac -- centripetal acceleration
11
Captain Chip, the pilot of a 60,500 kg plane, is
told that he must remain in a holding pattern
over the airport until it is his turn to land.
(a) What is the nature of centripetal force acting
on the plane?
(b) If Captain Chip flies his plane in a circle
whose radius is 50.0 km once every 30.0 min,
what is the size of the centripetal force?
12
13
Missy's favorite ride at the amusement park is a ride
called "Rotor". The Rotor has a radius of 4.0 m and it
takes a ride 2.0 sec to complete one full revolution.
(a) What is Missy's linear/tangential speed on the Rotor?
(b) What is Missy's centripetal acceleration on the Rotor?
(c) If Missy's mass is 55 kg, what is the value of the
normal force acting on her?
(d) If the coefficient of friction between Missy and the
wall is 0.65, find the magnitude of the force of friction.
(e) Is the frictional force large enough to keep Missy
"glued" to the wall of the Rotor?
14
15
16
17