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Rolling


Sriman Dutta
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Hello,

I'm new here.

 

Can anyone check these equations if they are correct.

 

Rolling velocity

Without friction - v=gt sin x

With friction - v=gt(sin x- ucos x)

 

x is angle of inclination and u is frictional coefficient and t is time taken and g is acceleration due to gravity.

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Is this homework?

 

You really need to explain the problem more completely otherwise people are left guessing what you mean.

 

I am guessing that you are talking about a ball rolling down a slope from a standing start so the equation of constant acceleration applies with the downslope acceleration = gsin(x) so we have using

 

vt = u + ft = 0 + gsin(x) * t

 

Which is your first equation.

 

But will the ball roll or slide down the slope?

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You gave two situations I started with the first and simplest.

 

What causes the ball to roll if there is no friction?

 

post-74263-0-65065800-1471254475.jpg

 

In the real world, air friction would be enough to turn it, but in our idealisation there are no such forces acting.

 

Note that a vehicle or railway engine wheels will spin under the vehicle when driven from the centre axle without moving the vehicle if there is not enough friction.

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Is this homework?

 

You really need to explain the problem more completely otherwise people are left guessing what you mean.

 

I am guessing that you are talking about a ball rolling down a slope from a standing start so the equation of constant acceleration applies with the downslope acceleration = gsin(x) so we have using

 

vt = u + ft = 0 + gsin(x) * t

 

Which is your first equation.

 

But will the ball roll or slide down the slope?

 

" vt = u + ft = 0 + gsin(x) * t "

 

Surely that would be the equation of a block/ball sliding down a frictionless slope. A ball rolling down a slope has a complete other factor to be considered - which your other points show you are keeping in mind - and which I will not spoil the fun by mentioning.

 

To give a hint: create your model based on conservation of energy, consider at start of experiment a still ball at height h1 and at the end a rolling ball at h2.

 

Hint 2 - it is not the same as the frictionless slope equation given above

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You're editing wikipedia without the first idea of the topic?

 

Think of a frictionless slope and a natural frictional slope. In one case the ball will slide down - in the second it will roll down. They are NOT the same situation. I suggested an energy audit - did you give it a go? Did you answer Studiot's question of why the ball rolls?

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Certainly, the body will slide if there is no friction. But, we think that some imaginary force F acts on the body thereby creating a couple, causing rotation, we can surely accept it as rolling without friction. I agree that situation is only imaginable and not practical. For the real world, the second equation should be apt.

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Certainly, the body will slide if there is no friction. But, we think that some imaginary force F acts on the body thereby creating a couple, causing rotation, we can surely accept it as rolling without friction. I agree that situation is only imaginable and not practical. For the real world, the second equation should be apt.

 

Nah. A body that goes from stationary to rotating (whether or not there is additional linear motion as well) has changed measurably - imaginary forces do not cut it; you need to have force applied over a distance and thus work to do an energy audit. If it is sliding with no friction, or sliding with some friction then you have one simple case - but rolling brings a completely new element to the model which must be accounted for properly; you have not done this

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