Equation for torque of a cylinder, a hollow cylinder, and a sphere.

In summary, the equation for torque on a cylinder is T = F * r * sin(theta), and for a hollow cylinder it is T = F * (r<sub>2</sub> - r<sub>1</sub>) * sin(theta). The equation for torque on a sphere is the same as for a cylinder. The torque equation can be rearranged to solve for the force or distance, and the angle between the force and the lever arm determines the direction and magnitude of the torque.
  • #1
nlingraham
16
0

Homework Statement



What is the equation for the torque of a cylinder, a hollow cylinder, and a sphere rolling down an incline?

Homework Equations



This is what I don't know

The Attempt at a Solution



I have no idea where to start.
 
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  • #2
Torque is the rate of change of angular momentum

if angular momentum = Iω, that is torque then?
 
  • #3
What is the equation for torque? Similarly to F = ma, the equation for torque is
[tex]T[/tex] [tex]=[/tex] [tex]I[/tex][tex]\alpha[/tex]
 
  • #4
Thanks, you guys are awesome
 

1. What is the equation for calculating torque on a cylinder?

The equation for torque on a cylinder is T = F * r * sin(theta), where T is the torque, F is the force applied, r is the distance from the axis of rotation to the point where the force is applied, and theta is the angle between the force and the lever arm.

2. How is the torque equation for a hollow cylinder different from that of a solid cylinder?

The equation for torque on a hollow cylinder is T = F * (r2 - r1) * sin(theta), where r2 is the outer radius and r1 is the inner radius. This is because the force is applied at a different distance from the axis of rotation for a hollow cylinder compared to a solid cylinder.

3. What is the equation for torque on a sphere?

The equation for torque on a sphere is T = F * r * sin(theta), where r is the radius of the sphere. This is the same equation as for a cylinder, as the shape of the object does not affect the torque.

4. Can the torque equation be used to find the force or distance instead?

Yes, the torque equation can be rearranged to solve for the force or distance. To find the force, the equation is F = T / (r * sin(theta)). To find the distance, the equation is r = T / (F * sin(theta)).

5. How does the angle between the force and the lever arm affect the torque?

The angle between the force and the lever arm, represented by theta in the torque equation, determines the direction of the torque. A larger angle will result in a smaller torque, while a smaller angle will result in a larger torque. This is because a force applied at a right angle to the lever arm will have the greatest effect on rotation.

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