MadSci Network: Physics

Re: How do I calculate how much energy is transmitted to a wheel of a bicycle?

Date: Mon Feb 5 18:24:51 2007
Posted By: Joel Chapman, Undergraduate, Mechanical Engineering, NC State
Area of science: Physics
ID: 1170557436.Ph

I assume that when you say "to the rear wheel" instead of "to the bike"
that you are referring to the rotational kinetic energy of the rear wheel
and not the actual motion of the bike itself.  If the bike is moving, you
are doing an experiment which will not appropriately answer your question,
because the energy transferred to the rear wheel is being transferred into
the bike's motion.  That would tell you how much energy is transmitted to
the kinetic energy of the bike's translational movement.  

The information you have...

"how many times the wheel rotates, the 
circumference of the wheel, and that for one rotation the bike moves 2 meters?"

Is insufficient to find the energy translated to the rear wheel.  You need
to know the mass of the rear wheel to find how much energy is in that wheel
while it is spinning.

The formula for rotational kinetic energy is ".5 * I * w^2" where I is the
moment of inertia and w (that's supposed to be a lowercase "omega") is the
rotational speed in radians per second.  There are 2pi radians per
rotation, so you need to convert rotations into radians to do the calculations.

For a wheel like this one, you can assume that all the mass is on the outer
edge.  Thus, the moment of inertia is M * R^2 (That's mass multiplied by
the radius squared).  Mass should be in kilograms, radius of the wheel
should be in meters.  

Once you've calculated a moment of inertia and a rotational speed in
radians, you can plug them in the rotational kinetic energy formula, and
that will tell you how much kinetic energy was transferred to the rear
wheel.  The answer would be in Joules.

If you make the assumption that all of the energy put into pedaling the
bike makes it to the rear wheel and that none of it is turned into heat via
friction, you can simply calculate the energy based on the force you put
into pedaling.  Energy equals force times distance, so if you apply a force
of 100 Newtons (that's about 25 pounds) through a distance of one full
pedal rotation (let's say it's two meters), then you would have transferred
(100 * 2) Joules or 200 Joules into the bike.  However, keeping a constant
force on the pedals would be difficult, because pedals move through a
circular motion.  Also, energy WOULD be lost to heat because of friction.

If you use the wheel's rotational speed, the bike must be still with the
rear wheel suspended.  If the bike moves, you've got another aspect of
energy transfer to deal with.

You will need to take off the wheel and weigh it to do this properly. 
Don't forget to convert the weight into kilogram mass.

You've only got about two days to do the experiments and get everything
together, so you'll probably need to hurry!

Hope this helps,


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