Download Circular Motion

Circular Motion
• An object that revolves about a single axis
undergoes circular motion.
• The axis of rotation is the line about which the
rotation occurs.
• Tangential speed (vt) describes the speed of an
object in circular motion. It depends on the
distance from the object to the center of the
circular path.
Ex: merry-go-rounds, carousel horses,
amusement park rides – the outside
object has a greater tangential speed.
Circular Motion
• When the tangential speed is constant, the
motion is described as uniform circular
motion.
• So when an object is moving in circular
motion, even if the tangential speed is
constant, the object is accelerating.
• The object is accelerating because it is
constantly changing direction.
Circular Motion
• The acceleration of an object in circular motion is
called centripetal acceleration (ac).
Centripetal acceleration = (tangential speed)2
radius of circular path
ac = vt2/r
The direction of centripetal acceleration is towards
the center of the circle.
Circular Motion
Ex: A car moves at a constant speed around a
circular track. If the car is 48.2 m from the track’s
center and has a centripetal acceleration of 8.05
m/s2, what is the car’s tangential speed?
G: r = 48.2 m
ac = 8.05 m/s2
U: vt
E: ac = vt2/r
S: 8.05 m/s2 = vt2/48.2 m
S: vt = 19.7 m/s
Circular Motion
• The inertia of an object traveling in a circular which pulls
the object into continuing in a straight line path. However
there are forces acting on the object as it moves around.
• Centripetal force (Fc) is the net force that is directed
toward the center of the circle. It is in the same direction
as the centripetal acceleration.
• Centripetal force is the net force towards the center of the
circular path followed by an object moving in uniform
circular motion.
Ex: this can be the force of a string on a rotating ball,
the gravitational force keeping the moon in orbit,
or the friction between a racecar’s tires and the
track
Circular Motion
• Centripetal force is necessary for circular
motion – the force changes the direction of
the velocity. If there were no centripetal
force, the object would continue on a straight
line path that is tangent to the circle.
Circular Motion
Fc = mac
So therefore:
Fc = mvt2/r
Centripetal force= mass x (tangential speed)2
radius of circular path
Circular Motion
Ex: A pilot is flying a small plane at 56.6 m/s in a circular
path with a radius of 188.5 m. The centripetal force
needed to maintain the plane’s circular motion is 1.89 x
104 N. What is the plane’s mass?
G: vt = 56.6 m/s
S: m = Fcr/vt2
r = 188.5 m
m = [(1.89 x 104 N)(188.5 m)]
Fc = 1.89 x 104 N
(56.6 m/s)2
U: m
S: m = 1110 kg
E: Fc = mvt2/r