Download Circular Motion Notes

Circular Motion Notes
Uniform Circular Motion – is the movement of an object at constant speed around a
circle with a fixed radius.
Centripetal Acceleration – The acceleration of an object in uniform circular motion. The
centripetal acceleration always points towards the center.
ac = v2/ r
Where ac = centripetal acceleration
v = tangential velocity
r = radius
Centripetal Force – The net force acting toward the center of a circle to keep an object
moving in a circular path.
Fc = mac or Fc = mv2/ r
Where m = mass
ac = centripetal acceleration
r = radius
v = tangential velocity
Critical velocity – The minimum velocity required for a satellite to travel a circular path
of radius r.
vc = (rg)
Where r = radius (m)
g –acceleration due to gravity
Critical velocity – The maximum speed a car can safely round a curve.
vc = (rg)
Where: r = radius
 = coefficient of friction
g –acceleration due to gravity
The number of g’s an object experiences. #g’s = acceleration/ 9.8
Circumference of a circle: c = 2r
Period of a pendulum: The time for a pendulum to make one complete oscillation.
T = 2(L/g)
Where: T = Period of a pendulum (s)
L = Length of a Pendulum (m)
g –acceleration due to gravity (m/s2)
Example1. It takes a 615 kg racing car 14.3 seconds to travel at a uniform speed around a
circular racetrack of 50.0 meters radius.
a. What is the acceleration of the car?
b. What average force must the track exert on the tires to produce this
acceleration?
Example 2. An athlete whirls a 7.00 kg hammer tied to the end of a 1.3 m chain in a
horizontal circle. The hammer moves at the rate of 1.0 rev/s.
a. What is the centripetal acceleration of the hammer?
b. What is the tension in the chain?
Example 3. A teacher is twirling his keys (m = 100g) in a vertical circle attached to a key
chain 5cm long. If the tension in the bottom of the chain is 4N, what is its
uniform speed? What is the tension at the top of the chain?
Example 4. A ball at the end of an 80 cm string is being whirled in a vertical circle. At
what minimum velocity will the string begin to go slack at the top of the
ball’s path?
Example 5. The coefficient of static friction between a car’s tire and a certain concrete
road is 1.0 when the road is dry and 0.7 when the road is wet. If the car can
safely make the turn at 25 mi/h on a dry day, what is the maximum velocity
on a rainy day?
Example 6. What is the length of a pendulum having a period of 3 seconds where gravity
is 9.8 m/s2
Example 7. A pendulum 110 cm long has a period of 2.1 seconds. If the value of gravity
is decreased by 75%, what would be the period?