Calculating Centripetal Force for Circular Motion: Tips and Tricks

[oneplusone]

Hello,

I'm having trouble with solving for the centripetal force.
Some questions in my textbook don't give the velocity and radius, so the centripetal force is a bit harder to calculate. There are three main scenarios which I am having trouble with:

[1] A girl has a ball in her hand connected to a string. The ball travels in a circular path, such that the plane of the circle lies perpendicular to the plane of the earth.

[2] A girl now swings the ball in a circular path, so the plane is parallel to the earth.

[3] A car drives a long a raceway in a circular loop.


For each of these scenarios, what would be the centripetal force and how would you solve for it, generally?

I'm having trouble solving for this, especially when trig functions are used.

Thanks, and any help would be great!

 

[SW VandeCarr]

Hello,

I'm having trouble with solving for the centripetal force.
Some questions in my textbook don't give the velocity and radius, so the centripetal force is a bit harder to calculate.
[reat!

For any force, generally, you need the mass and the acceleration. In the case of centripetal force the acceleration is toward the center of rotation. Note dimensionally for F=ma F=MLT^{-2}=ML^2T^{-2}L^{-1} or F= mv^2/r where r is the radius of rotation. You may need to calculate the force using radians/sec or the angular acceleration and translate to SI depending on what you are given. As for swinging a ball on a string in a plane perpendicular to the earth, it seems it's a wash, gravity helping half the time and retarding half the time, so I think the net effect is zero. In the case of being in the "plane" of the earth, you would simply add the force vectors and get the resultant vector.

 

[oneplusone]

Hello,

thanks for the reply. Could you explain the variables M,L,T?

 

[SW VandeCarr]

Hello,

thanks for the reply. Could you explain the variables M,L,T?

M=mass L=length T=time. These are the fundamental dimensions for all SI units in mechanics. So velocity is L/T.

 

[rcgldr]

There's isn't sufficient information in the 3 problems to provide an exact answer. For all of the problems, the speed and the radius are unspecified. For the first problem, you need to know the speed at a specific point as the ball moves in a vertical circle, since it's speed changes, slowest at the top, fastest at the bottom.

For the second problem, if given the angle of the string, that angle can be used to determine centripetal acceleration instead of speed and radius.

 

[oneplusone]

If the radii are specified, and the speed aren't, how would you solve the first case?

I kind of understand the [2]nd scenario, however gravity's affect in the 1st confuses me.

 

[SW VandeCarr]

If the radii are specified, and the speed aren't, how would you solve the first case?

I kind of understand the [2]nd scenario, however gravity's affect in the 1st confuses me.

You do need the speed which would be variable in the first (vertical) example, although the relative effect of gravity diminishes with speed. However, why wouldn't the g forces cancel out? The average speed would be the basis for calculating the force. If you don't know the speed (velocity) you need know the acceleration as well as the mass to calculate the force. Alternatively you could calculate the force from the radius, rpm and the mass.

Are you sure a numerical solution was requested? Perhaps they just wanted the direction of the resultant force vector.

 

[oneplusone]

Thanks for the reply.

This wasn't a question in my textbook, just a general case which I've observed a lot of problems to be in.

 

[SW VandeCarr]

Thanks for the reply.

This wasn't a question in my textbook, just a general case which I've observed a lot of problems to be in.

OK. So now I'll ask you about the direction of the force vector and of the velocity vector describing the object in circular motion.