Transcript Rotational Mechanics Torque

Rotational
Mechanics
Torque is “turning force”
T = F r or Force times the lever arm radius
(also may be written T = F d or T = F L)
For Maximum Torque…
• You must apply the force at a RIGHT
ANGLE to the lever arm
• (any other angle lessens the torque)
• The true formula is
Τ = F r (sin θ )
• Since the sin of a 90 degree θ is _____ ,
this all makes perfect sense ;-)
If you double the lever arm
distance, you________ the Torque
The English unit for
torque is the FootPound (ft lb)
The metric unit for
torque is the
Newton-meter (N m)
One child weighs 400 N and sits 1.5 meters
from the fulcrum (pivot point or center) of the
see saw. How much torque does he produce?
His little sister weighs only 300 N. How far must
she sit from the fulcrum to be balanced?
SOLUTIONS
T = F d or F r or F l
1) T = 400 N (1.5 m) = 600 N m of Torque
2) T = T so Fd = Fd
• 400 N (1.5 m) = 300 N (x)
• 600 N m = 300 N (x)
• 600 N m = x = 2 m
• 300 N
Link to Torque
All torques are CLOCKWISE or
COUNTERCLOCKWISE
What are ways
you can
INCREASE
TORQUE?
ROTATIONAL INERTIA
Once something is
spinning, it naturally
______________________.
Rotational inertia
basic formula:
I=mr2
Formula varies for
different shapes and
distributions of mass!
• The bigger the radius, the HIGHER the rotational
inertia
• The more MASS is AWAY FROM the axis of
rotation, the HIGHER the rotational inertia
1. What would have a higher
rotational inertia, a regular
basketball filled with air, or a
basketball filled with foam?
2.
3.
4.
5.
6.
Which would accelerate faster (or
win a race down a short ramp)?
Which would tend to keep rolling
longer (or win a race down a long
ramp or distance?)
Which is easier to start spinning?
Which is easier to stop spinning?
Which tends to keep spinning
longer?
• Example: Assuming the earth is a
solid sphere rotating around an
axis through its poles, the
rotational inertia of the earth would
be:
I = 2/5 mr2 =
2/5 (5.98 x 1024 kg) (6.37 x 106 m)2
=
9.71 x 1037 kg m
Link
• Why do you bend your
legs when you run?
• Does it take more torque
to move long legs, or short
legs?
• Does it take more torque
to move bent legs or
straight legs?
• Does it take more torque to turn
big wheels/tires or small? Why?
• Would you get better gas mileage
around town with big wheels/tires
or small? Why?
• Would you get better gas mileage
on a long deserted highway trip
through flat country with big
wheels/tires or small? Why?
• Why do you hold your arms
out when walking across a
log or balance beam?
• How does holding a
pole help?
• Do the buckets make
the pole have a higher
rotational inertia, or
lower?
• Does the pole tend to
twist (get off balance)
more easily if buckets
are empty or full?
To INCREASE his rate of spin, what does
the skater do?
Does this INCREASE or DECREASE his
rotational inertia?
If a diver, gymnast, etc., goes from an
extended to a tucked (balled up)
position:
1)Does their rotational inertia
INCREASE, DECREASE, OR STAY
THE SAME?
2)Does their angular velocity
INCREASE, DECREASE, OR STAY
THE SAME?
3)Does their angular momentum
INCREASE, DECREASE, OR STAY
THE SAME?
• Remember that linear momentum is
(p = mv)
• Angular momentum is
(L = mvr or L = Iω)
• Angular momentum is ALWAYS
CONSERVED, just like linear momentum
• Iω = Iω
•I
ω = Iω
• If rotational inertia increases,
what happens to rotational speed?