Is tangential force the same as centripetal force?

[michelle90]

Homework Statement

Rotor blades attatched to a disc rotate.
The rotor blades rotate at a speed of 15574rpm. The blades are 220mm from the centre of the disc.

These blades are attatched to a disc that is 400mm in diameter.
A force of 8kN/rad acts upon the blades and 600N/rad. (see picture)


Calculate the tangential blade loading.

Not too sure if centripetal force is the same as tangential force though?

Homework Equations

(itex)f=mv^2/r(/itex)

The Attempt at a Solution

First calculated the centrifugal acceleration

(itex)=Mω^2r(/itex)
Centrifugal acceleration = 53197m/s

Then find the centrifugal force

(itex)f=mv^2/r(/itex)

I have the velocity and can obtain the mass and radius.

I'm not so sure this is the right way to solve the tangential blade loading??
I need to find angular acceleration?

Thanks for the in advance help guys.

 

[rcgldr]

A centripetal force is a force perpendicular to the instantaneous velocity of a point on the rotors. A tangental force is a force in the directioni (or exactly opposite of the direction) of a point on the rotors.

A force of 8kN/rad acts upon the blades and 600N/rad.

What does the ".../rad" mean in this problem statement?

 

[michelle90]

It means per radian.

So to calculate the tangential force I would need to angular velocity and then use the formula:

$Pr=I_oa$

 

[rcgldr]

What does the ".../rad" mean in this problem statement?

It means per radian.

So the force is a function of radians and is increasing as the rotors rotate, so at 0 radians, the force is 0, at 1 radian, the force is 8kN, at 2 radians, the force is 16kN, ... . Are you sure this is what the problem intended?

 

[michelle90]

So the force is a function of radians and is increasing as the rotors rotate, so at 0 radians, the force is 0, at 1 radian, the force is 8kN, at 2 radians, the force is 16kN, ... . Are you sure this is what the problem intended?

The problem is to find the force acting on the circumference of the disc.
There are blades that attach to this disc which make up a rotor blade.
The forces shown (in the .jpg ) are those acting upon the blades.

 

[rcgldr]

What does the ".../rad" mean in this problem statement?

It means per radian.

The problem is to find the force acting on the circumference of the disc. There are blades that attach to this disc which make up a rotor blade.
The forces shown (in the .jpg ) are those acting upon the blades.

The ".../rad" doesn't make sense. I think that the problem statement and the diagram should not have that ".../rad" component, in which case, at 220mm from the center of the disc, you have 8kN of centripetal force and 600N of tangential force. I'm not sure what the term "tangential blade loading" means. I did a web search for "blade loading" and I see math involving "tangential mean swirl velocity".

 

[haruspex]

The ".../rad" doesn't make sense.

I believe it is treating the blades - presumably narrow and numerous - as a continuum. In a sector of angular width δθ, the centripetal load is 8000 δθ N.
I don't understand the diagram. What part of the blade attaches to the disc, and how? It sounds like the outer end of the blade extends 20mm beyond the disc, but in that case I'm not sure why the disc diameter matters.
To have any hope of answering this question, you need a clear definition of what is meant by "tangential blade loading". How is it different from the 600N/rad given? Or maybe that multiplied by 2pi? I can't find one.