Undergrad Coriolis effect and the acceleration experienced in a rotating frame

[member 743765]

Is the reason behind coriolis acceleration is that as you move far from the centre of a rotating frame the tangential velocity increases?

 

[Orodruin]

If by "tangential velocity increases" you mean "the tangential velocity of a fixed point in the rotating frame relative to an inertial frame", yes, partially. It describes the Coriolis effect when you move radially. If you move tangentially it is the effect of moving with/against the rotation.

 

[PeroK]

Not really. The Coriolis force depends on the velocity in a rotating reference frame:

https://en.m.wikipedia.org/wiki/Coriolis_force

 

[member 743765]

If by "tangential velocity increases" you mean "the tangential velocity of a fixed point in the rotating frame relative to an inertial frame", yes, partially. It describes the Coriolis effect when you move radially. If you move tangentially it is the effect of moving with/against the rotation.

But what do u mean moving tangentially I think in that case your velocity wouldn't be constant so it is always true I think

 

[Orodruin]

Constant in what frame?

 

[member 743765]

Constant in what frame?

I mean consider a rotating disk it consists of infinite concentric circles so any linear uniform motion will take you from one circle to another so the radius of rotation changes and the tangential speed increases

 

[member 743765]

I mean consider a rotating disk it consists of infinite concentric circles so any linear uniform motion will take you from one circle to another so the radius of rotation changes and the tangential speed increases

Linear uniform motion relative to the noninertial frame

 

[Orodruin]

I mean consider a rotating disk it consists of infinite concentric circles so any linear uniform motion will take you from one circle to another so the radius of rotation changes and the tangential speed increases

But as I said, this does not explain the part of the Coriolis effect when you move along one of the circles. If you move along a circle in the direction of rotation, you will be pushed outwards by the Coriolis effect. If you move against the direction of rotation, you will be pushed inwards.

On a merry-go-round in the night,
Coriolis was shaken with fright.
Despite how he walked,
'Twas like he was stalked,
By some fiend always pushing him right.
https://www.physics.harvard.edu/undergrad/limericks

 

[member 743765]

But as I said, this does not explain the part of the Coriolis effect when you move along one of the circles. If you move along a circle in the direction of rotation, you will be pushed outwards by the Coriolis effect. If you move against the direction of rotation, you will be pushed inwards.

On a merry-go-round in the night,
Coriolis was shaken with fright.
Despite how he walked,
'Twas like he was stalked,
By some fiend always pushing him right.
https://www.physics.harvard.edu/undergrad/limericks

My friend moving along one of the circles means there is acceleration relative to the noninertial frame (centripetal)

 

[PeroK]

My friend moving along one of the circles means there is acceleration relative to the noninertial frame (centripetal)

What is the point of this thread?

Coriolis and centripetal acceleration are not mutually exclusive.

 

[Orodruin]

My friend moving along one of the circles means there is acceleration relative to the noninertial frame (centripetal)

No. In the rotating frame, there are two non-inertial contributions to the radial force. One is the centrifugal effect, which only depends on the distance from the rotational center, but the Coriolis effect also plays a role if an object is moving along one of the circles as seen in the rotating frame.

Consider an object at rest in the inertial frame. Such an object will move in circles in the rotating frame, meaning that the net force must be a centripetal force of appropriate size. However, the centrifugal force is pointing outwards, not inwards, and therefore cannot supply that centripetal force. The centripetal force for such an object (as seen in the rotating frame) comes from the Coriolis effect, which supplies an inward force of twice the magnitude of the Coriolis force, because the object is moving tangentially in the rotating frame.

 

[A.T.]

My friend moving along one of the circles means there is acceleration relative to the noninertial frame (centripetal)

But the required centripetal force changes when he moves tangentially in the rotating frame, and that modification of the required centripetal force coresponds to the radial Coriolis force.

From a previous thread:

One intuitive way to think about the radial Coriolis force, is as a velocity dependent modification of the centrifugal force. In fact you could order the inertial force terms in a rotating frame by direction, and lump the radial Coriolis force with radial centrifugal force together. But for mathematical and historical reasons we separate them as position dependent term (centrifugal) and a velocity dependent term (Coriolis).

https://www.physicsforums.com/threa...ed-by-tangential-velocity.977984/post-6238568

 

[member 743765]

Okay but I thought that if the particle is rotating so it has centripetal acceleration relative to noninertial frame the force here is real not fictitious and thats what I meant

 

[A.T.]

Okay but I thought that if the particle is rotating so it has centripetal acceleration relative to noninertial frame the force here is real not fictitious and thats what I meant

Yes, but to make Newton 2nd Law work in the rotating frame you introduce a inertial centrifugal force that balances the real centripetal force for objects at rest in the rotating frame. But if they move tangentially in the rotating frame, the centripetal force is different and so you need a velocity dependent radial inertial force term to make Newton 2nd work again. That is the radial Coriolis force.

 

[sophiecentaur]

What is the point of this thread?

The Maths of the topic are hardly a matter for dispute.

Imo, the thread (argument) has taken off because the question has been interpreted in more than one way. In a rotating frame, the coriolis 'force' only manifests itself when you try to move. When you're stationary (in the frame), you only experience the (reaction to) the centrifugal force. The coriolis force gives two different experiences when on a rotating disc; when you are not connected to the disc, your path over the surface (a thrown object perhaps) will be a curve which you interpret as a force, pushing you off course. Very non-newtonian behaviour for a free object. When you move along a straight rail, you experience an tangible sideways force. (I realise that the true Physicists amongst us will say they are the same thing but intuition often conflicts with Maths). When you are on a playground roundabout and you try to move your arm, you have no idea about your 'course'; all you feel is a very noticeable force when you try to move your arm. Kids know no maths; ask them about what they feel on a roundabout.