# Motion

Can rectilinear motion be thought of as a circular motion with radius of curvature that tends to infinity. Note by Sai Prasanth Rao
6 years ago

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Can $1$ be thought of as $0.99999999999999999.........................................$ ?

- 6 years ago

yes if there are infinite number of 9's

- 6 years ago

As far as i think rectilinear motion can not be considered as circular motion, because with an infinite radius and using the formula $v=\omega r$, even for a little bit of an angular velocity, our linear velocity should turn out be infinite which is not true, as it is possible to measure a speed of a moving car but not of infinity...

Moreover $0.9999999.....\infty$ tends to one, but considering it as one is an approximation, i.e. $0.99999....\infty \approx 1$, not an equality...:)

- 6 years ago

When you say 0.99999.. with a large number of 9's it would tend to 1 but when you say infinite number of 9's it should be equal to 1 as it is an infinite G.P. As far as the note is concerned, a circle with infinite radius would give an object zero angular velocity. Another example-A polygon with infinite sides is a circle.

- 6 years ago

You said it yourself...zero angular velocity and an infinite radius, how will you define their product i.e. Linear velocity, because you can't define $0\times \infty$

- 6 years ago

however we can define the formula (m)(v^2)/r. As r is infinity the accelaration is zero. However how is it possible that in this way we get zero centripetal accelaration and in your method we get undefined centripetal accelaration.

- 6 years ago

In my way, you don't get undefined centripetal acceleration, Although you get an undefined linear velocity. And moreover using $\frac { m{ v }^{ 2 } }{ r }$ , we see that an object moving in a circle must have a centripetal force. But, in this case, the centripetal force is zero, which clearly signifies that the object is not in circular motion

- 6 years ago

yes we can conclude that the object is not in circular motion if we use the formula mv^2/r, but why can't we conclude the result while using the formula (mw^2)r

- 6 years ago

Yes you can, as you can see 2 formulas of the same quantity are condradicting each other. That means that our earlier assumption that an object moving linearly is a part of a circle with an infinite radius is wrong...

- 6 years ago

which standard are you in?

- 6 years ago

11, is there anything wrong?

- 6 years ago