We know that every burnout results in at least one angry bystander because science tells us that every action generates an equal and opposite reaction. Newton’s Third Law also states that the torque that propels your car creates a reactionary force that acts on the Earth’s surface. Geologically speaking, you’re insignificant, and that force is minuscule. But what if we launched every car on the planet, all at once? Could a coordinated effort to accelerate every car extant, in the same direction at the same instant, substantially alter the speed of the Earth’s rotation?
If you’re at the equator, the Earth’s 24-hour revolution means you’re moving at a linear speed of roughly 1070 mph, but this number isn’t constant. The 2011 earthquake in Japan redistributed enough mass to shorten the day by about 1.8 microseconds. Due to conservation of momentum, every force on the Earth’s surface has some effect on its rotation. However, if we want the change to be more than trivial, we’ll need enormous forces due to the Earth’s prodigious moment of inertia.
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This wildly impractical exercise requires several assumptions only vaguely grounded in reality. We estimate the number of roadgoing vehicles on Earth at 1 billion, although the people who track these things claim that number was exceeded in 2011. Let’s also simplify each of these vehicles to an “average” car that makes 120 pound-feet of torque, rides on 205/45R-16 tires, and connects the engine to the wheels via a torque-multiplying 12.6:1 ratio (first gear times the final-drive ratio). To ensure that the reactionary force is maximized with the longest lever arm and oriented perpendicular to Earth’s axis, we propose driving every car to the equator and pointing them due west. And while the idea of a 1-billion-car synchronized burnout makes us giddy, our math assumes perfect traction, so that each car’s peak torque is fully transferred to the Earth’s surface. Below, we show our work:
The laws of physics state that a body’s angular acceleration is the quotient of the torque applied to the body divided by its moment of inertia.
Variables Key
Aa = angular acceleration of the Earth
Al = linear acceleration at the equator
Dr = car-to-Earth drive ratio, the 20,924,640-foot radius of the average tire, 2.5 x 107
I = Earth’s moment of inertia, 5.92 x 1037 slug-square feet
N = number of cars, 1,000,000,000
R = Earth’s radius, 3963 miles or 2.09 x 107 feet
T = duration of our full-throttle acceleration, 1 second
Tm = torque multiplication through the transmission and final drive, 12.6
Tq = each car’s torque, 120 pound-feet
V = change in the Earth’s velocity at the equator
In our example [See Variables Key, above],
Multiplying this angular acceleration by Earth’s radius yields linear acceleration at the equator:
Therefore, for one second of full-throttle acceleration, the change of the Earth’s velocity at the equator is:
In other units, our billions cars increase Earth’s rotational speed by just 0.00000000001 mph. What’s more, we can’t permanently alter that rotation unless our 1 billion cars continue their westward acceleration. The forces that bring the cars to a stop slow the planet back to its original speed. But wasn’t that fun while it lasted?
from Car and Driver Blog http://ift.tt/1vBdeSY
via Agya
