Transcript AcaDec - University of Arizona

Science w/ Ms. Hendryx
11/8/11
Spinning things!!!
Everything that spins/twists/rotates involves circular
motion. One way to describe the size of a circle is by
its radius, r. So to deal with circular motion, we’re
going to throw in the radius of the imaginary circle
about which an object is moving (r has units of
length, like meters).
1.Torque (rhymes with fork): how much you
can twist/be twisted using a given amount of
force. torque = F*r (r = radius)
I’m changing a tire: if I need 20 N*m of torque to loosen
the lug nut with a wrench, how much force to I have to
apply if my grip on the wrench is 5 cm from the nut
(convert to meters)? What if I hold the wrench 0.5 m
from the nut? *Hint: the nut is the center of your circle
of motion, and the distance from the nut to your hand is
the radius of that circle.
In your book, they say angular momentum (L) is
moment of inertia (I, corresponds to mass) times
angular velocity (ω).
So if you can remember p = mv, you can
remember L = I ω. The only difference is that the
angle of motion is changing (hence the circle).
What is the angular momentum of an ice skater
whose moment of inertia is 2.5 kg*m spinning with an
angular velocity of 5 m/s?
We know that acceleration causes velocity to change
with time, right? Well now the velocity is changing by
changing direction, not speed.
So if you swing a rock on a string, the acceleration is
toward your hand. That means the centripetal force is
also toward your hand.
a
a
v
v
And the velocity doesn’t change as much if the string is
longer (the circle is bigger), so the acceleration
decreases as radius increases: acent = v2/r.
(Think curves in a go-kart—do you feel the tight turns
more or less?)
*Important note: “velocity” is distance per time.
“Angular velocity” is angle per time.
(Think ceiling fan.)
If a softball pitcher has a 2.5-ft. arm (r), what
is the centripetal acceleration of the ball if
the pitch is a 60 mile-per-hour fast ball?
A softball pitcher has a 2.5-ft. arm (r)
We can still use Newton’s 2nd Law, so Fcent = macent.
What is the centripetal force the pitcher above is
applying to the ball? Assume the ball weighs 1lb, and
include units.