Key Concepts:

Terms in this set (56)

A constant force is applied to a pedal causing it to rotate. The pedal is fastened to a gear so that the gear and pedal rotate at the same speed. The pedal gear is connected to a rear gear via a chain. In the same way that the first gear is fastened to the pedal so to is the rear gear attached to the back wheel[via the axle]. As a result, the rear gear and rear wheel will also rotate at the same speed. Since the bike was initially at rest the gears[& wheels] all experience an increase in rotational speed until a maximum value is reached that depends on the tangential chain speed. Once this maximum chain speed is reached, the bike will not move any faster on this gear. The chain is then moved to the next gear witch has a smaller radius. This action has two effects. (1) The tangential speed of the chain decreases & (2) the bike becomes more difficult to pedal. The chain speed decreases because of the decrease in gear radius. Tangential speed is the product of the radius & (rotational) angular speed. Both gears have the same rotational speed because they are fixed into the axis. However the second gear is smaller and thus has a smaller radius value, thus a smaller tangential speed. As for the 2nd effect, the bike becomes more difficult to pedal because more Force is required to get the object to rotate. Torque equals the product of Force & radius. A bike requires a certain torque value to achieve the maximum tangential chain speed. Let's consider a hypothetical bike where 10 units of torque are needed to get to the maximum tangential speed. When we shift to the smaller gear the value of torque decreases. [For our hypothetical bike, let's say it decreases to 6 units of torque]. If the rider wants to maintain the 10 units of torque that he was at before shifting gears he must now exert a larger force because he is limited by the fact that the radius of the new gear is smaller. If he were to continue to exert the same force, the bike would slow down. To get back up to the 10 units of torque, the rider exert more force [or experiences more resistance] on the pedal.