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Uniform circular motion
• What’s uniform?
• What direction is the velocity?
• What direction is the acceleration?
• What’s the magnitude of the acceleration?
In one second:
In one second:
In one second:
v
What is the acceleration?
In one second:
ac
What is the acceleration?
What if the speed is doubled?
In one second:
In one second:
In one second:
In one second:
v
2v
ac
What if the radius is halved?
In one second:
What if the radius is halved?
In one second:
What if the radius is halved?
In one second:
What if the radius is halved?
In one second:
ac
What if the radius is halved?
In one second:
r
r/2
Centripetal Acceleration
• acceleration for objects moving in a circle
at constant speed
• perpendicular to the velocity, which points
towards the center of the circle
• ac = v2/r
The Rotor
What direction is the
net force on the ball?
Free-body diagram:
Ball
??
TS,B
WE,B
If you can’t label the force,
it probably doesn’t belong
on your diagram!
Free-body diagram:
Ball
TS,B
WE,B
Free-body diagram:
Ball
TS,B
WE,B
Free-body diagram:
Ty
Ball
Tx
WE,B
What direction is the
net force on the ball?
Ty
Ball
Tx
WE,B
What direction is the
net force on the ball?
Ty
Ball
Tx
WE,B
a
For an object moving in a
circle:
• the acceleration points towards the center of
the circle, and
• the NET FORCE points towards the center of
the circle.
• We give a special name to this NET FORCE;
we call it the CENTRIPETAL FORCE.
Which force is the
NET FORCE?
Ty
Ball
Tx
WE,B
a
What about the centrifugal
force?
• There is no such force, regardless of what
Mr. Wizard says.
Bucket of water problem
• You swing a bucket of water (m=1kg) in a
vertical circle at constant speed, which we’ll
estimate. What is the normal force by the
bottom of the bucket on the water at:
a. the top of the circle, and
b. the bottom of the circle.
FBD at top
water
WE,W
What else?
water
NB,W
WE,W
What direction is a?
v
a
a
water
NB,W
WE,W
Why doesn’t the water
fall on Greg’s head?
But, how big is a?
v
a
a
water
NB,W
WE,W
Why doesn’t the water
fall on Greg’s head?
Centripetal acceleration
• aC = v2/r ≈ 36 m/s2
1m
• Assume r = 1 meter
• need to find v
Assume t = 1 sec;
2
p
r
≈ 6 m/s
v=
t
Question
a = aC
water
NB,W
WE,W
In one second:
In one second:
In one second:
v
What is the acceleration?
In one second:
ac
What is the acceleration?
Apply Newton’s 2nd Law
a
= 36 m/s2
water
NB,W
WE,W = m g = 10 N
What’s wrong with this
freebody diagram?
Fnet = (1 kg) (36 m/s2)
= 36 N
What if we swing a little
slower?
a
water
NB,W
WE,W
What if we swing a little
slower?
a
water
NB,W
WE,W
What has to change on the
FBD?
a
water
NB,W
WE,W
What has to change on the
FBD?
a
water
NB,W
WE,W
What changes at the
bottom?
a
water
NB,W
WE,W
At the bottom:
a
NB,W
water
WE,W
At the bottom:
a
NB,W
water
WE,W
Apply Newton’s 2nd Law
a
NB,W
= 36 m/s2
water
WE,W = m g = 10 N
How big is the
normal force?
Fnet = (1 kg) (36 m/s2)
= 36 N