precal question - Tilted Forum Project Discussion Community

khuct · 05-15-2004, 10:18 PM

Q) You are riding a bicyle along a level road. Assume each wheel is 28 inches in diameter, the rear spocket has radius 3 inches and the front sprocket has radius r inches. Suppose you are pedaling the front sprocket at the rate of 1.5 rev/sec and your forward speed is 11pmh on the bike. What is the radius of the front sprocket?

I'm been stuck on this question for awhile..any help?

pig · 05-17-2004, 08:18 AM

khuct : I've played around with this problem, and I feel like there is some assumption or bit of knowledge that I'm not privy to. Here's my thinking, tell me if I'm missing something - apparently the physics of bikes is beyond me.

1. The rate of forward speed should equal the rotational speed of the front tire, multiplied by it's circumference. Also, it seems to me that if sprocket on the front tire rotates as fast as the rim of the tire, so if the sprocket goes at 1.5 rev/sec, then so does the 28 in outer diameter, and thus it seems to me like the problem is overspecified, and that 1.5 rev/sec times 28*pi*conversion factor better equal 11 miles per hr. There must be a piece of information that eludes me.

Peetster · 05-17-2004, 08:25 AM

The rear and front sprocket are not rotating at the same rate, but they do have the same rotational velocity. Hope that helps.

Peetster · 05-17-2004, 11:38 AM

Think of two barrels, one twice as large as the other, on their sides with an axel through the middle. There is a hamster running on top of each barrel. The hamsters are running at the exact same speed. The smaller barrel will rotate much faster, because it has a smaller circumference.

Replace the hamsters with a chain. The chain has a set velocity, bit the two differently sized sprockets will rotate at different rates.

pig · 05-17-2004, 01:16 PM

Peetster : Thanks for the tip. For your amusement, allow me to share the following :

Imagine trying to solve this problem, such that you were under the impression that the bike was some sort of Circe-du-Soleil freak contraption, such that you were literally pedalling the sprocket of the front wheel, of unknown radius, at a constant rate of 1.5 rev/sec, whilst this sprocket was attached by chain to a sprocket of radius 3 on the rear wheel, which is spinning at wanton like a drunk 15 year-old whore. That is what my former mathematics worked out to be. Thanks for your time - I certainly do feel bettter.

05-15-2004, 10:18 PM	#1 (permalink)
khuct Upright	precal question Q) You are riding a bicyle along a level road. Assume each wheel is 28 inches in diameter, the rear spocket has radius 3 inches and the front sprocket has radius r inches. Suppose you are pedaling the front sprocket at the rate of 1.5 rev/sec and your forward speed is 11pmh on the bike. What is the radius of the front sprocket? I'm been stuck on this question for awhile..any help?

05-17-2004, 08:18 AM	#2 (permalink)
pig pigglet pigglet Location: Locash	khuct : I've played around with this problem, and I feel like there is some assumption or bit of knowledge that I'm not privy to. Here's my thinking, tell me if I'm missing something - apparently the physics of bikes is beyond me. 1. The rate of forward speed should equal the rotational speed of the front tire, multiplied by it's circumference. Also, it seems to me that if sprocket on the front tire rotates as fast as the rim of the tire, so if the sprocket goes at 1.5 rev/sec, then so does the 28 in outer diameter, and thus it seems to me like the problem is overspecified, and that 1.5 rev/sec times 28piconversion factor better equal 11 miles per hr. There must be a piece of information that eludes me. __________________ You don't love me, you just love my piggy style

05-17-2004, 01:16 PM	#5 (permalink)
pig pigglet pigglet Location: Locash	Peetster : Thanks for the tip. For your amusement, allow me to share the following : Imagine trying to solve this problem, such that you were under the impression that the bike was some sort of Circe-du-Soleil freak contraption, such that you were literally pedalling the sprocket of the front wheel, of unknown radius, at a constant rate of 1.5 rev/sec, whilst this sprocket was attached by chain to a sprocket of radius 3 on the rear wheel, which is spinning at wanton like a drunk 15 year-old whore. That is what my former mathematics worked out to be. Thanks for your time - I certainly do feel bettter. __________________ You don't love me, you just love my piggy style

05-17-2004, 08:25 AM	#3 (permalink)
Peetster Right Now Location: Home	The rear and front sprocket are not rotating at the same rate, but they do have the same rotational velocity. Hope that helps.

05-17-2004, 11:38 AM	#4 (permalink)
Peetster Right Now Location: Home	Think of two barrels, one twice as large as the other, on their sides with an axel through the middle. There is a hamster running on top of each barrel. The hamsters are running at the exact same speed. The smaller barrel will rotate much faster, because it has a smaller circumference. Replace the hamsters with a chain. The chain has a set velocity, bit the two differently sized sprockets will rotate at different rates.