Calculating Torque to Move Object

[gearhead]

I have a bicycle with 26 inch diameter wheels that weighs 200 pounds with the rider on it. the bicycle has two wheels. How much torque would this bicycle need to maintain a constant speed of 20mph? Assuming no air resistance?

 

[berkeman]

I have a bicycle with 26 inch diameter wheels that weighs 200 pounds with the rider on it. the bicycle has two wheels. How much torque would this bicycle need to maintain a constant speed of 20mph? Assuming no air resistance?

What do you think? Is there any other form of rolling resistance to be overcome by this torque?

Is this homework/coursework? If so, I can move this thread to the Homework Help forums. In any case, we don't solve homework-type questions here on the PF. Show us your thoughts and calculations, and we can provide some hints and tutorial help.

 

[astrokreng]

To calculate the torque needed to maintain a constant speed of 20mph on the bicycle, we need to consider the rotational motion of the wheels. The torque required is directly proportional to the angular acceleration of the wheels and the moment of inertia of the wheels and rider system.

First, we need to calculate the moment of inertia of the system. This can be done using the formula I = m*r^2, where m is the mass of the system (200 pounds or 90.7 kg) and r is the radius of the wheels (13 inches or 0.33 meters).

I = (90.7 kg)*(0.33 m)^2 = 9.46 kg*m^2

Next, we need to convert the speed of 20mph to meters per second (m/s) for the angular acceleration calculation. 20mph is equivalent to 8.94 m/s.

Now, we can use the formula torque = I*angular acceleration to calculate the torque needed.

torque = (9.46 kg*m^2)*(8.94 m/s^2) = 84.6 N*m

Therefore, the bicycle would need a torque of 84.6 N*m to maintain a constant speed of 20mph, assuming no air resistance. This torque can be achieved by pedaling with a certain force at a specific distance from the center of the wheels, or by using gears to increase the torque output of the rider.