Uniform Circular Motion
• Constant speed, but change direction  acceleration.
• If acceleration net force.
• If motion in circle at const speed, force towards the center.
Centripetal (center seeking) acceleration
ac = v2 / r
A puck is traveling at a constant speed around a circle on a table.
What would we have to know to find the tension in the string?
v2
FC   Ftowards center  m ac  m
r
Clicker!
You are whirling a tennis ball on a string around in circles when the string suddenly
snaps. What direction does the tennis ball fly? (the figure below is a top view).
The ball will fly along a tangential direction.
Clicker!
You are whirling a 0.5 kg ball on a string around in circles. If the radius of the circle
is 1m, and the ball takes 1s to complete a circular path, what is the speed of the ball?
(1)
(2)
(3)
(4)
(5)
1 m/s
2 m/s
4p m/s
2p m/s
4p2 m/s
1m
v = 2pr/T = (2p * 1m )/1s = 2p m/s
Clicker!
You are whirling a 0.5 kg ball on a string around in circles. If the radius of the circle
is 1m, and the ball takes 1s to complete a circular path, what is the centripetal
acceleration of the ball?
(1)
(2)
(3)
(4)
(5)
1 m/s^2
2 m/s^2
4p m/s^2
2p m/s^2
4p2 m/s^2
1m
a = v2/r = (2p2 m/s)/ 1m = 4p2 m/s^2
Clicker!
You are whirling a 0.5 kg ball on a string around in circles. If the radius of the circle
is 1m, and the ball takes 1s to complete a circular path, what is the centripetal force
experience by the ball?
(1)
(2)
(3)
(4)
(5)
1N
2N
2p2 N
2p N
4p2 N
1m
Fc = m ac = 0.5 kg * 4p2 m/s^2 = 2p2 N
Clicker!
A puck of mass 0.25kg is tied to a string and allow to revolve in a
circle of radius 1.0m on a frictionless tabletop. The other end of the
string passes through a hole in the center of the table, and a mass of
0.5kg is tied to it. The suspended mass remains in equilibrium
while the puck on the table revolves. What is the tension in the
string?
(1) 0.25 g = 2.45 N (2) 0.75 g = 7.35 N
(3) 0.5 g = 4.9 N (4) None of the above.
T
T = mg = 0.5 kg . 9.8 m/s^2 = 4.9 N
Because the same rope is tied to the puck, the tension
is the same along the rope.
Clicker!
A puck of mass 0.25kg is tied to a string and allow to revolve in a
circle of radius 1.0m on a frictionless tabletop. The other end of the
string passes through a hole in the center of the table, and a mass of
0.5kg is tied to it. The suspended mass remains in equilibrium
while the puck on the table revolves. What is the centripetal force
experienced by the puck?
(1) 0.25 g = 2.45 N (2) 0.75 g = 7.35 N
(3) 0.5 g = 4.9 N (4) None of the above.
Fc
T
Because the same rope is tied to the puck, the tension
is equal to the centripetal force of the puck.
Clicker!
A puck of mass 0.25kg is tied to a string and allow to revolve in a
circle of radius 1.0m on a frictionless tabletop. The other end of the
string passes through a hole in the center of the table, and a mass of
0.5kg is tied to it. The suspended mass remains in equilibrium
while the puck on the table revolves. What is the centripetal
acceleration experienced by the puck? (Tension = 4.9 N)
(1) 19.6 m/s^2
(3) 30 m/s^2
(2) 9.8 m/s^2
(4) 2 m/s^2.
Fc = m ac . Therefore, ac = Fc/m
= 4.9 N/ 0.25 kg
= 19.6 m/s^2
Clicker!
A puck of mass 0.25kg is tied to a string and allow to revolve in a
circle of radius 1.0m on a frictionless tabletop. The other end of the
string passes through a hole in the center of the table, and a mass of
0.5kg is tied to it. The suspended mass remains in equilibrium
while the puck on the table revolves. What is the speed of the
puck?
(1) 19.6 m/s
(3) 30.0 m/s
(2) 4.4 m/s
(4) 3.4 m/s.
ac = v2/r
v = a r = 19.6 m/s^2 * 1.0 m = 4.4 m/s
Clicker!
A motorcycle stunt driver performs a vertical loop the loop as shown. Which point
will have the largest centripetal force ?
(5) The same centripetal force
at all points.
W
FN
FN
W
At (3), Fc = FN +W
At (1), Fc = FN -W
Curved Paths
• Curved paths can be considered as small parts of circles.
ac
Satellites
• gravity is only force causing centripetal acceleration
F
R
 maC
M Em
v2
Fc = G 2  m
• r to centerrof circle
r
• Independent of mass of satellite
Example.
What will be the speed of a satellite orbiting 100 km above the Earth
surface?