I just watched an awesome YouTube video by
Veritasium, an awesome YouTube channel similar to Vsauce, that specializes in
physics and cool demonstrations. In the video, we were shown a 40-pound
barbell, but attached only on one side. The metal bar used to lift the weight,
instead of having a round 20-pound weight at either side, had only one 40-pound
weight, on the left side.
Even when a muscular
bodybuilder was brought in, nobody could lift this strange barbell from the
side opposite the round weight, and keep it horizontal. Why? Simple mechanics
tells us that torque, τ, is equal to
the lever arm, b, times the force, F:
Having a large weight, F = 40 lbs., and a relatively long lever
arm, b = 3 ft., τ = 120 lbs. × ft. In order to counteract this huge
torque against your hand and keep the bar level, your hand, with a width = 5 in.
≅ 0.416 ft., would have to apply a huge force.
From the first formula, we can derive that
,
so the force your hand
would need is 120 lbs. × ft. ÷ 0.42
ft. ≅ 290 lbs.. In
conclusion, in order to hold this barbell horizontally, you would have to be
able to lift almost 300 lbs. with that hand.
The next thing that
happened in the video is that the circular weight, which had been attached as a
flywheel to the bar, was spun up to about 3000 rpm., the weight being about 5
in. in radius. When the barbell is released, and held up only from the arm on
the side opposite the spinning weight, the spinning weight exhibits a few
properties of a gyroscope.
First off, it
opposes any change in its angular orientation. The first thing we need to
calculate this is the weight’s moment of inertia, l, given by
where M is the mass, 40 lbs., and R is the radius, 5 in.. This gives a
moment of inertia of 500 lbs. × ft2.. The next thing we need is the
angular velocity, α, given by
where F is the gravitational attraction, 32.2
ft. / second2, M is the
mass, and R is the radius. This
formula gives us an angular velocity of 0.322. Next, we must find the angular
velocity, ω, which is, in this case,
which means that ω ≅ 9424.78 rad. × sec.-1.
Now, we can finally
calculate the torque that the spinning weight exerts upon the bar, using the
following formula:
This gives us a torque,
τ, of about 44,413,239,185.2 lbs. of force. WOW! Over 4.4 BILLION POUNDS of
force! That’s how strongly the spinning weight is holding itself up!
So, when the bar is
being held from the side opposite the spinning weight, any gravitational pull
on the weight is cancelled out instantly by its enormous opposition force. The
40-pound barbell has become literally lighter than a feather!
See the Video: https://www.youtube.com/watch?v=GeyDf4ooPdo
For more information,
visit: http://en.wikipedia.org/wiki/Gyroscope
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