Formulas for torque and velocity in simple algebra

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misty
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Ok I am a high school freshman and haven't actually studied physics yet, but I'm trying to learn the formulas needed for a project I'm working on. ( I didn't know if this should go here or in the homework section, since it isn't really for a school assignment, but please move it if it belongs there.)

Given a wheel with a radius of R1 that has a mass of M1. Every 45 degrees there is a bucket attached who's center of gravity is at a radius of R2, with a mass of M2, and another bucket who's center of gravity is at a radius of R3, with a mass of M3.

The wheel is spinning clockwise, and the buckets around R2 are constantly being filled, with sand, of a mass of M4, when they are at the top (0 degrees). When they reach the bottom (180 degrees) they are emptied. Also The buckets around R3 re constantly being filled, with sand, of a mass of M5, when they are at 90 degrees, and emptied at 270 degrees. Assume the wheel is spinning perpetually, that there is no force of impact when the buckets are filled with sand, and that there is no other source of energy.

What I need to know is how, using simple algebra, do I calculate:
1) the torque
2) the rotational velocity (rpm)
3) the horse power
 
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misty said:
Ok I am a high school freshman and haven't actually studied physics yet, but I'm trying to learn the formulas needed for a project I'm working on. ( I didn't know if this should go here or in the homework section, since it isn't really for a school assignment, but please move it if it belongs there.)

Given a wheel with a radius of R1 that has a mass of M1. Every 45 degrees there is a bucket attached who's center of gravity is at a radius of R2, with a mass of M2, and another bucket who's center of gravity is at a radius of R3, with a mass of M3.

The wheel is spinning clockwise, and the buckets around R2 are constantly being filled, with sand, of a mass of M4, when they are at the top (0 degrees). When they reach the bottom (180 degrees) they are emptied. Also The buckets around R3 re constantly being filled, with sand, of a mass of M5, when they are at 90 degrees, and emptied at 270 degrees. Assume the wheel is spinning perpetually, that there is no force of impact when the buckets are filled with sand, and that there is no other source of energy.

What I need to know is how, using simple algebra, do I calculate:
1) the torque
2) the rotational velocity (rpm)
3) the horse power

I don't see this being very intuitive for you without having spent some time on physics...

Torque = r*F*sin(theta)

where r is the distance from the pivot to the point where you want the torque, F is the force applied at that distance point, and theta is the angle between the direction of F and the direction of object of length r

rotational velocity is literally rotations/time (a rotation is one full revolution of an object)

power = torque*rotational speed... you'll have to check your units to convert it to horsepower, which is just one type of power

more specifically:

1 hp = 33,000 ft·pound/minute where ft/min comes from your rotational velocity and pounds comes from your force.
 
Pythagorean said:
I don't see this being very intuitive for you without having spent some time on physics...

Torque = r*F*sin(theta)

where r is the distance from the pivot to the point where you want the torque, F is the force applied at that distance point, and theta is the angle between the direction of F and the direction of object of length r

rotational velocity is literally rotations/time (a rotation is one full revolution of an object)

power = torque*rotational speed... you'll have to check your units to convert it to horsepower, which is just one type of power

more specifically:

1 hp = 33,000 ft·pound/minute where ft/min comes from your rotational velocity and pounds comes from your force.

Thanks for the reply but it doesn't really address the question at hand. I'm not looking for a general texbook formula for velocity and torque, I'm looking how to calculate it from the variables of my example. r*F*sin(theta) is only usefull if you know how to derive F and sin(theta). The variables I know are the multiple masses, and radial distances, and I need to be able to determine what the various forces acting on them are and in what direction. I also need to be able to determine how the forces amply or diminish each other.

So for me, Torque = r*F*sin(theta) is a question, not an answer.
 
That's what I'd suspected. Study some basic physics on your own or maybe somebody else will help you. If you have any specific questions, I'll help you to understand a piece at a time, but I won't break down the whole problem for you anymore than I have.