Finding Inclination of Rod on Cylinder to Wall

In summary, to find the inclination of a rod on a cylinder to the wall, you can use the formula tan(theta) = (h/r) or a protractor to measure the angle directly. This information is significant in determining stability and balance of the rod, and can change over time. Tools such as a measuring tape, protractor, level, or plumb line may be needed to find the inclination. This concept can also be applied to other objects and is useful in various fields.
  • #1
Suvadip
74
0
A smooth circular cylinder of radius \(\displaystyle b\) is fixed parallel to a smooth vertical wall with its axis horizontal at distance \(\displaystyle c\) from the wall. A smooth uniform heavy rod of length \(\displaystyle 2a\) rests on the cylinder with one end on the wall in a vertical plane perpendicular to the wall. Show that its inclination \(\displaystyle \theta\) to the horizontal is given by

\(\displaystyle a\cos^3\theta+b\sin^3\theta=c\)

Please help
 
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  • #2
Re: statics

Two things:

1. Could you please post a picture of the situation?

2. Could you please show what work and ideas you've had?
 

Related to Finding Inclination of Rod on Cylinder to Wall

1. How do you find the inclination of a rod on a cylinder to the wall?

To find the inclination of a rod on a cylinder to the wall, you can use the formula tan(theta) = (h/r), where theta is the inclination angle, h is the height of the rod from the ground, and r is the radius of the cylinder. You can also use a protractor to measure the angle directly.

2. What is the significance of finding the inclination of a rod on a cylinder to the wall?

The inclination of a rod on a cylinder to the wall can provide important information about the stability and balance of the rod. It can also help determine the angle at which the rod should be placed to ensure maximum support and prevent it from slipping or falling.

3. Can the inclination of a rod on a cylinder to the wall change over time?

Yes, the inclination of a rod on a cylinder to the wall can change over time due to various factors such as changes in the structure of the cylinder or wall, external forces acting on the rod, or wear and tear of the rod itself. It is important to regularly check and adjust the inclination as needed.

4. Are there any tools or equipment needed to find the inclination of a rod on a cylinder to the wall?

To find the inclination, you will need a measuring tape or ruler to measure the height of the rod and the radius of the cylinder. You may also need a protractor to measure the angle directly. Additionally, having a level or plumb line can help ensure accurate measurements.

5. Can the inclination of a rod on a cylinder to the wall be applied to other objects?

Yes, the concept of finding inclination can be applied to other objects as well, such as a ladder against a wall or a ramp on a hill. It is a useful tool for ensuring stability and safety in various structures and can be applied in different fields such as engineering, construction, and physics.

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