Download Circular motion and Centripetal Acceleration

Circular
Motion
Uniform circular motion: examples
include
•Objects in orbit (earth around the sun
•Driving a car around a corner
•Rotating a ball around on a string
Circular Motion
c
Circular Motion
 According
to Newton’s mechanics,
objects don’t tend to move in a circle by
themselves. They tend to either be at rest
of move in a straight line at constant
speed (this is Newton’s first law)
Circular Motion
 Circular
motion is not “natural” motion
 Something (a Force) must make an object
move in a circle
 The Force causing circular motion can be
one of many different forces, depends on
the situation (orbit = gravitational force,
car turning a corner = frictional force
between tires and the road, ball on a
string = tension force)
Circular motion
example
Circular motion: car
travelling around a corner
F
is friction
Example of circular motion
 Now
gravity is influencing circular motion
Circular Motion
 Remember
from Newton’s 2nd law, that
…..Force = mass x acceleration (F = ma)
 But if the object is in uniform circular
motion, their speed is constant, so is
acceleration = 0?
Circular Motion
 In
circular motion, the acceleration is a
change in the direction of the object,
even though the speed is constant, the
direction keeps changing, and velocity is
a vector.
 The force keeps pulling the object to the
center, hence we call this type of
acceleration “centripetal” acceleration
which means “center seeking”.
Circular Motion
 Solving
circular motion problems is like a
typical “force” problem where the motion
is circular rather than linear.
 F = ma still works, now we have a new
term for centripetal acceleration
 ac = v2/r acceleration (centripetal) =
velocity squared/radius.
Uniform circular motion
 Centripetal
acceleration
Circular Motion
 Example
….. Ball on a string rotating
horizontally
 Let’s say it’s a 1 kg ball rotating at 4
m/s at a radius of 0.5m. What is the
Force of tension in the string?
 Find the acceleration of the ball where
a = v2/r
 Using the idea that F=ma and that the
Force causing circular motion is the
tension in the string.