CIRCULAR MOTION
> An object moving in a circle experiences an acceleration towards
the center of the cirle of motion. This is called centripetal acceleration.
It can be calculated by squaring the velocity and dividing that by the
radius of the circle:
ac = v2/r
> The time it takes for an object to make one complete revolution is
called the period. The velocity of an object moving in a circle (with
a radius of r) is equal to the circumference of the circle (2*PI*r) divided
by the period, T. You may use 3.14 for pi (PI), or the entire value
in your calculator.
v = (2*3.14*r) / T OR this can
be simplified to: v = 6.28* (r/T)
> By combining these two equations, we can say:
ac = (4*PI2*r)
/ T2 OR ac = 39.4*(r/T2)
> Since Newton's second law says that a mass undergoing acceleration
generates a force, we can say that the centripetal acceleration creates
a centripetal force, which also acts towards the center of the circle of
motion.
Fc = m*ac
= (m*v2)/r = (m*4*PI2*r) / T2
CHANGING CIRCULAR MOTION: TORQUE
> Force applied in a rotational motion produces torque. Torque
is the product of the force applied and the distance of the applied force
from the center of rotation.
T = F * d
> If you have two rotational forces acting in opposite directions on
a point, there is no movement only if the torques of the two are equal
and opposite.
HARMONIC MOTION
> Harmonic motion can be described as a back and forth motion, such
as in a vibrating guitar string, a pendulum, and a spring. If the
restoring force (force that tries to return the object back to the equilibrium
position) varies linearly with the displacement, the motion that is produced
is called simple harmonic motion. The period (T) is the time it takes
for one complete back and forth movement. The amplitude is the maximum
distance the object moves from the equilibrium position.
> For a pendulum, the only variables used in computing the period are
the length of the pendulum and gravity.
_____
T = 2*PI*\/L/|g|
To simplify this equation, assuming PI = 3.14 and g = - 9.8 m/s/s,
you get
__
T = 2 \/ L OR
L = T2/2
> For a spring,
|
