Q: If the pedal sprocket (radius $4.03$ in) is rotated through $180^ ext{o}$, what is the length of chain moved by the pedal sprocket?

$4.03\times\pi$ in$\div1$ (i.e., half a rotation: $4.03\times\pi$ in)

Q: If the chain moves $4.03\times\pi$ in, how many rotations does the rear sprocket (radius $1.35$ in) make?

$(4.03\times\pi)/(2\pi\times1.35)$

Q: If the pedal sprocket rotates $180^ ext{o}$, what is the total distance the bicycle moves? (Pedal sprocket radius $4.03$ in, rear sprocket radius $1.35$ in, wheel radius $13.9$ in)

$(4.03\times\pi)/(2\pi\times1.35)\times2\pi\times13.9$ in

Question 1

A bicycle's chain drive has a pedal sprocket radius of 4.03 in, a rear wheel sprocket radius of 1.35 in, and a wheel radius of 13.9 in. If the pedals are rotated through $180^	ext{o}$, how far does the bicycle move forward? (Assume no slippage and that the chain transmits all pedal rotation to the wheel.)

Accepted Answer

$176.0$ in

Question 2

If the pedal sprocket (radius $4.03$ in) is rotated through $180^	ext{o}$, what is the length of chain moved by the pedal sprocket?

Accepted Answer

$4.03	imes\pi$ in$\div1$ (i.e., half a rotation: $4.03	imes\pi$ in)

Question 3

Given the pedal sprocket radius is $4.03$ in and the rear wheel sprocket radius is $1.35$ in, what is the gear ratio (pedal sprocket to rear sprocket)?

Accepted Answer

$4.03/1.35$

Question 4

If the chain moves a distance $d$ when the pedals rotate $180^	ext{o}$, how many rotations does the rear wheel sprocket make? (Pedal sprocket radius $4.03$ in, rear sprocket radius $1.35$ in)

Accepted Answer

$d/(2\pi	imes1.35)$

Question 5

If the rear wheel rotates $n$ times, and the wheel radius is $13.9$ in, what is the total distance the bicycle moves?

Accepted Answer

$n	imes2\pi	imes13.9$

Question 6

Which of the following best describes the relationship between pedal rotation and bicycle movement distance?

Accepted Answer

The distance moved depends on the ratio of pedal sprocket to rear sprocket radii and the wheel radius.

Question 7

If the pedal sprocket radius is doubled while keeping the rear sprocket and wheel radii the same, what happens to the distance the bicycle moves for a fixed pedal rotation?

Accepted Answer

It is doubled.

Question 8

Suppose the rear wheel radius is increased to $27.8$ in (double the original $13.9$ in), with all other parameters unchanged. For the same pedal rotation, how does the distance moved change?

Accepted Answer

It is doubled.

Question 9

A cyclist wants to maximize the distance traveled per pedal rotation. Which adjustment would be most effective?

Accepted Answer

Increase the pedal sprocket radius and the wheel radius.

Question 10

If the pedal sprocket radius is $4.03$ in and the rear sprocket radius is $1.35$ in, what is the angular velocity ratio between the pedal and rear sprocket?

Accepted Answer

$1.35/4.03$

Question 11

If the pedals are rotated through $360^	ext{o}$, how far does the chain move around the pedal sprocket (radius $4.03$ in)?

Accepted Answer

$4.03	imes2\pi$ in

Question 12

If the rear wheel rotates once, what is the linear distance the bicycle moves? (Wheel radius $13.9$ in)

Accepted Answer

$2\pi	imes13.9$ in

Question 13

If the pedal sprocket radius is $4.03$ in and the rear sprocket radius is $1.35$ in, how many times does the rear wheel rotate for one full pedal rotation?

Accepted Answer

$4.03/1.35$

Question 14

If the pedals are rotated through $180^	ext{o}$, what fraction of a full pedal rotation is this?

Accepted Answer

$1/2$

Question 15

If the pedal sprocket radius is $4.03$ in, what is the circumference of the pedal sprocket?

Accepted Answer

$2\pi	imes4.03$ in

Question 16

If the rear sprocket radius is $1.35$ in, what is the circumference of the rear sprocket?

Accepted Answer

$2\pi	imes1.35$ in

Question 17

If the pedal sprocket rotates $180^	ext{o}$, what is the arc length traced by a point on its rim? (Radius $4.03$ in)

Accepted Answer

$4.03	imes\pi$ in

Question 18

If the chain moves $4.03	imes\pi$ in, how many rotations does the rear sprocket (radius $1.35$ in) make?

Accepted Answer

$(4.03	imes\pi)/(2\pi	imes1.35)$

Question 19

If the rear wheel rotates $n$ times, and the wheel radius is $13.9$ in, what is the total distance the bicycle moves?

Accepted Answer

$n	imes2\pi	imes13.9$ in

Question 20

If the pedal sprocket rotates $180^	ext{o}$, what is the total distance the bicycle moves? (Pedal sprocket radius $4.03$ in, rear sprocket radius $1.35$ in, wheel radius $13.9$ in)

Accepted Answer

$(4.03	imes\pi)/(2\pi	imes1.35)	imes2\pi	imes13.9$ in

Applications of Circular Motion: Bicycle Chain Drive Problem

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