# Does the centripetal force $= mg - R$?

Please tell me if I'm wrong with an explanation (A Level explanation please).

You feel the heaviest at the bottom of the ferris wheel because in order for there to be a centripetal force, the normal force has to increase to provide the force. Therefore, your weight decreases because Newton Third's Law states that the two pairs of forces are opposite and equal. (But I didn't think it was possible to decrease your weight and so I think I am wrong). You feel the lightest or weightless at the top of the ferris wheel because the centripetal force required is opposite to the normal force, thus the normal force needs to decrease in order to provide a force for the inward acceleration. As the normal force decreases, your weight must therefore also decrease and therefore you feel weightless.

I have a feeling this is wrong because you can't physically change your weight on Earth (unless you exercise) and so can someone provide me with some explanation as to why you feel weightless.

Oh, and does the centripetal force $$= mg - R$$?

Edit: I now understand that weight and the normal reaction force are not an interaction pair so Newton's Third Law does not apply.

So, does this mean that the circular motion is due to the normal reaction force only increasing?

• What is $R$? Usually it means "radius," but you can't do addition or subtraction between a quantity with units of force, like $mg$, and a quantity with units of length.
– rob
Aug 29, 2020 at 19:33
• A lot of people have no idea what "A-level" means, other than perhaps it's above "B-level".
– JEB
Aug 29, 2020 at 20:49

Your body constituents is what gives your body 'mass'. But the weight you feel is not a direct result of your mass itself. Since you understand what normal force is, you should be able to understand that when you stand on the ground, the earth pulls you down with a force equal to 'm times g', which is your weight; but the reason you 'feel' this weight is because the ground is there between you and the centre of the earth. Therefore, you exert a force of 'm times g' on the ground, and by Newton's Third Law, the ground exerts an equal and opposite normal force on your feet; that pressure is what makes you feel weight all over your body.

So the feeling of weight, or weightlessness depends on the normal force exerted on you by whatever surface you happen to be standing on, not your mass(of course your mass directly affects it, but not what causes it). Like you have mentioned, the normal force at the bottom of the Ferris wheel is highest, and lowest at the top. Relating to the above reasoning, you can figure out why you feel heavy at the bottom and light at the top. Centripetal force is 'mass times centripetal acceleration'=$$mv^2/R$$

• Please use MathJax for the formulas, e.g. \$=mv^2/R\$ would result in $=mv^2/R$. It looks much nicer, and is easier to read. :) Aug 29, 2020 at 20:34
• @fanyul Thanks will keep that in mind Aug 29, 2020 at 21:14
• Also you can edit your answers, if you would like to improve. (The edit button is at the bottom left corner of your post.) Aug 29, 2020 at 21:29
• Usually I wouldn't use the term 'centripetal force', it is a bit misleading in my opinion. For uniform circular motion the equation of motion is $\sum F=ma_\textrm{cp}(=mv2/r)$, so there has to be some kind of ('other'/'external') forces, which provide the centripetal acceleration ($a_\textrm{cp}$). Now there are two forces, so the EOM would be: $mg+N=ma_\textrm{cp}$. (Where $N$ is the normal/constraint force.) Aug 29, 2020 at 21:50

Many people confound mass and weight. Your mass is always the same, but the force on the mass by the gravity of the earth is even smaller at the poles than at the equator. In the bottom of the ferrywheel the force on your mass comes from the gravity, and a second force the centrifugal force in the same direction, so you feel heavier, on top of the wheel the weight you feel standing on the earth is diminished be the centrifugal force, with the right speed you can feel weightless, but your weight, the gravitational force ist the same, but the centrifugal force against this weight ensures , that you don't feel your "weight". The centrifugal force is m*v^2/R so it is not proportional to R.

• Thanks for your reply! So just to reiterate, the weight remains the same but the centrifugal force and the normal reaction force changes which is why you feel weightless/ heavier? Aug 30, 2020 at 11:09

Centrifugal force acts radially outwards on a Ferris wheel, gravity only pulls downward. Therefor centrifugal force is subtracted from gravity at the top, making you feel lighter, and added to gravity at the bottom, making you feel heavier.