Download Circular Motion ACT 1 Circular Motion Uniform Circular Motion

Circular Motion ACT 1
B
A
C
v
A ball is going around in a circle attached to a string. If the
string breaks at the instant shown, which path will the ball
follow?
Circular Motion
r
Position: r = constant
r
Speed:
v = constant
Uniform Circular Motion
T≡ period = the time required for one complete rotation.
v=
circumference 2π r
=
period
T
For a particle in uniform
circular motion, the velocity
vector v remains constant in
magnitude, but it continuously
changes its direction.
1
Acceleration in Uniform
Circular Motion
v2
∆v
v
R
v1
∆R
v2
v1
a=
v2
R
centripetal acceleration
aave= ∆v / ∆t
Acceleration toward center
Acceleration is due to change in direction, not
speed. Object turns “toward” center
∴ must be a force on object toward center.
12
Centripetal Acceleration
a =
v2
(centripetal acceleration)
r
v=
2π r
(tangential velocity)
T
Centripetal Acceleration ACT
Which motion has the largest centripetal acceleration?
2
Preflight
Consider the following situation: You are driving a car with
constant speed around a horizontal circular track. On a piece
of paper, draw a Free Body Diagram (FBD) for the car. How
many forces are acting on the car?
FN
A) 1
B) 2
C) 3
D) 4
0%
28%
44%
28%
f
correct
R
W
ΣF = ma = mv2/R
“Gravity, Normal Force, Friction”
“Fn = Normal Force, W = Weight, the force of
gravity, f = centripetal force.”
16
Common Incorrect Responses
• Acceleration: ΣF = ma
– Centripetal Acceleration
• Force of Motion (Inertia not a force)
– Forward Force,
– Force of velocity
– Speed
• Centrifugal Force (No such thing!)
– Centripetal (really acceleration)
– Inward force (really friction)
• Internal Forces (don’t count, cancel)
– Car
– Engine
Circular Motion Requires Net Force
Net force may be provided by the tension in a
string, the normal force, or friction, among other
sources – as with any net force.
3
Preflights
Consider the following situation: You are driving a car with
constant speed around a horizontal circular track. On a
piece of paper, draw a Free Body Diagram (FBD) for the
car. The net force on the car is FN
f
22% A. Zero
67% B. Pointing
11% C. Pointing
radially inward
radially outward
R
W
correct
ΣF = ma = mv2/R
“This is why many racetracks
have banked roadways”
“Centripetal force is always pointing inward"
“Ever spin stuff in a bowl? It gravitates outward.”
16
Dip ACT
Suppose you are driving through a valley whose bottom has
a circular shape. If your mass is m, what is the magnitude
of the normal force FN exerted on you by the car seat as
you drive past the bottom of the hill
A. FN < mg
a=v2/R
B. FN = mg
R
C. FN > mg
FN
v
mg
20
Merry-Go-Round ACT
• Bonnie sits on the outer rim of a merry-go-round with
radius 3 meters, and Klyde sits midway between the center
and the rim. The merry-go-round makes one complete
revolution every two seconds.
– Klyde’s speed is:
Klyde
Bonnie
(a) the same as Bonnie’s
(b) twice Bonnie’s
(c) half Bonnie’s
33
4
Banked Curves
Centrifuge
A centrifuge rotates at a rate such that the
bottom of a test tube travels at a speed of 89.3
m/s. The bottom of the test tube is 8.50 cm
from the axis of rotation. What is the centripetal
acceleration acp at the bottom of the test tube in
m/s and in g (where 1 g = 9.81 m/s2)?
5