{"id":3316,"date":"2021-07-19T17:21:15","date_gmt":"2021-07-19T11:51:15","guid":{"rendered":"https:\/\/acejee.com\/blog\/?p=3316"},"modified":"2024-09-30T08:10:45","modified_gmt":"2024-09-30T02:40:45","slug":"centrifugal-centripetal-forces","status":"publish","type":"post","link":"https:\/\/acejee.com\/blog\/centrifugal-centripetal-forces\/","title":{"rendered":"Centrifugal & Centripetal Forces"},"content":{"rendered":"\t\t
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Fictitious Forces | Centrifugal Force<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t
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A fictitious force is a force that ‘appears’ to act on a mass when it’s motion is described using an accelerating frame of reference. Note that the observer on the ground or non accelerating or inertial frame of reference would deny existence of these forces and he\/she will claim that the observer in the accelerating frame of reference has been deceived in believing that such a force exists. For example, in case of an airplane accelerating down the runway, an observer inside the airplane would claim that there is an invisible force is acting on the passengers and pushing them back into their seats\u00a0<\/p>

Now, centrifugal force is one such fictitious force that appears to act on objects when viewed by an observer in a rotating (accelerating) frame of reference.<\/p>

So, let’s take a look at some of the examples of such fictitious or imaginary forces, and then we will recap the differences between centripetal and centrifugal forces.<\/p>

Afterwards you will get to practice 10 questions,<\/b> where in you can solve for the unknown in inertial frame of reference (no centrifugal forces) or we can solve for them in non-inertial or accelerating frame of reference (wherein we will have centrifugal forces)<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Centrifugal force examples<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t
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Vehicle driving around a curve:<\/b>\u00a0When going around a curve the passengers inside the vehicle, say car, experience a fictitious radially outward force which in reality is their upper body trying to follow the straight line path but lower body due to radially inwards frictional force between car seat and the person is trying to move around the circular path<\/p>

Stone on a string<\/b>: When swinging a stone on a string in a circular path, a tension force develops in the string as if someone is pulling the stone radially outwards while in reality moving in a circle means that the particle is under centripetal acceleration ($= ]cfrac{v^2}{r}$) and so there must be a centripetal force to provide that acceleration else the stone will tend to fly off in a straight line path<\/p>

Weight of an object at the poles vs it’s weight at the poles<\/b>: Weight $N$ reported on the equator $=mg – m \\omega^2 r$, where $r$ is the radius of the earth while at poles it will be $= mg$. This is because part of the gravitational force $mg$ is consumed in turning the object along with the earth as it rotates with angular velocity $\\omega$<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Difference between centripetal and centrifugal Force<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t
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Centripetal Forces<\/u><\/b>:<\/p>

1. Real forces (for example tension in string or normal force or electrostatic force) pointed radially inwards i.e. towards the center
2. These forces are what turns the direction of velocity vector of the particle as it moves around a circular path
3. Observer in inertial frame of reference will write the newton’s 2nd law as
$F_{centripetal} = \\cfrac{mv^2}{r}$<\/p>

Centrifugal Forces<\/u><\/b>:<\/p>

1. Fictitious force as reported by observer in the accelerating frame of reference and they will appear to be pointed radially outwards
2. For the observer in the rotating frame of reference, the particle appears stationary and since it is stationary he\/she concludes that there must a fictitious force countering centripetal forces
3. Observer in non-inertial or rotating frame of reference will write the newton’s 2nd law as
$F_{net, \\ radial} = 0$
or
$F_{centripetal} + F_{centrifugal} = 0$
where
$F_{centrifugal} =$ $\\cfrac{mv^2}{r}$.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Practice Problems (involving use of fictitious force)<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t
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Now let’s solve the following problems in inertial as well as in non inertial frames of reference for better understanding.<\/p>

Once again note that in inertial frame of reference we will use $F_{net, \\ external} = m a_{centripetal}$ while in non inertial frame of reference, i.e. in the frame of reference of accelerating platform we will introduce centrifugal force $= -ma_{centripetal}$ and then solve the problem at hand<\/p>

Now, the following practice problems have been divided into 3 scenarios<\/p>

1) Linearly accelerating frame of reference: The platform is accelerating along a given direction and the given particle is moving along a straight line with respect to this accelerating platform<\/p>

2) Linear accelerating frame of reference:\u00a0The platform is accelerating along a given direction and the given particle is moving along a circular path with respect to this accelerating platform<\/span><\/p>

3) Rotating frame of reference : The platform is rotating about an axis and the given particle is either stationary or moving along a straight line with respect to this rotating platform.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Linearly accelerating platform | Translational motion of mass placed on the accelerating platform <\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t
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Q1 A block of mass $m$ is placed on an inclined plane. With what acceleration $a$, towards right, should the system move on a horizontal surface so that $m$ does NOT slide on the surface of the inclined plane? Assume all surfaces to be smooth.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\"Centrifugal\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t
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\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/i><\/span>\n\t\t\t\t\t\t\t\t<\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\tAnswer<\/a>\n\t\t\t\t\t<\/h3>\n\n\t\t\t\t\t

$a = g \\tan \\theta$<\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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