Jun
9
When you pedal a bicycle, maximum torque is produced when the pedal sprocket arms are in the horizontal positi?
When you pedal a bicycle, maximum torque is produced when the pedal sprocket arms are in the horizontal position, and no torque is produced when they are in the vertical position. Explain.
You can think of it one of two (related) ways, as far as I can tell. One is just the mathematical definition of torque, which is the cross product of the radial vector (the vector from the center of rotation to the point at which force is applied) and the force vector (the actual applied force). In general, the cross product of two vectors r and F is equal to |r|*|F|*sin(theta), where |x| implies the magnitude of the vector x, and theta is the angle between the vectors. The magnitude of the torque, therefore, depends on the magnitude of the sine function, which has its maximum (sin = 1) when theta is equal to pi/2, which is when the two vectors are perpendicular to one another (in the case of the bike, when the pedal is in the horizontal position, you are pushing down on the pedal, right? So, the force vector is down, and the radial vector, along the pedal, is horizontal. Thus, the two vectors are perpendicular, or orthogonal, as it’s called more generally). On the other hand, the sine function has its minimum magnitude (0) when theta = 0 (when the two vectors are parallel or anti-parallel – pointing opposite). This happens when the pedal is vertical (such as when it points straight up, because the force you’re applying is straight down, hence anti-parallel to the pedal).
Sorry about the long paragraph. The other way of thinking about it is that torque is a force that produces rotation. When you pedal a bike, most of the time, you are applying a force straight down, pushing the pedal. If you push straight down while the pedal points straight up, do you get any rotation? No, you have to push at a little bit of an angle to get the pedal to go around, right? So if there’s no rotation when the force and the pedal are vertical, there’s no torque. On the other hand, think about trying to loosen a bolt with a wrench. When you get the wrench on, do you normally push inward on the wrench? No, you push at a right angle to the wrench, right? Because that produces the MOST torque – when the force is perpendicular to the wrench. In the case of the bike, you’re normally pushing down, so you get the most torque when you’re pushing down on something that is oriented horizontally, so that your force is at a right angle to the pedal.
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