Circular Motion: What is the Radius of Curvature Near Maximum Height?

In summary, a stone is projected at an angle with the horizontal with velocity u and executes a nearly circular motion near its maximum height for a short time. The radius of the circular path exhibited by the stone at the top of its path can be found using the equation a_{radial} = \frac{v^2}{Radius}, where v is tangential to the curve and the speed at the top can be used to find the radius of curvature.
  • #1
vipulgoyal
26
0

Homework Statement



a stone is projected at an angle with the horizontal with velocity u. it executes a nearly circular motion near its maximum height for a short time. the radius of circular path is
??`

Homework Equations


answer is u2 sin2x/g3. The Attempt at a Solution
why isn't it is just the maximum height?
 
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  • #2


vipulgoyal said:
why isn't it is just the maximum height?

I can't understand what you are asking
 
  • #3


cupid.callin said:
I can't understand what you are asking

i just want to know the radius of the circular path exhibited by the stone at the top of its path

""why it isn't the maximim height"" i mean that answer should be the mximum height attained by the body
 
  • #4


no it won't be max height

like in this case:

attachment.php?attachmentid=33448&stc=1&d=1300916524.gif


H is max height but radius is R
 

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  • #5


cupid.callin said:
no it won't be max height

like in this case:

attachment.php?attachmentid=33448&stc=1&d=1300916524.gif


H is max height but radius is R

yeah... thnx

but still don't know how to find R ??
 
  • #6


(Its late now ... must sleep or take steroids :zzz:)

use the eqn:

[tex]a_{radial} = \frac{v^2}{Radius}[/tex]

and here v will be tangential to the curve obviously

(off to sleep :zzz:)
 
  • #7


thnx man.. jus got it right
 
  • #8
hi vipulgoyal! :smile:

it is asking you for the radius of curvature at the top

hint: what is the speed at the top? :wink:
 

FAQ: Circular Motion: What is the Radius of Curvature Near Maximum Height?

What is circular motion?

Circular motion is a type of motion where an object moves along a circular path. This path can be either a perfect circle or an oval-like shape, also known as an ellipse. In circular motion, the object's velocity is constantly changing, but its speed remains constant.

What is centripetal force?

Centripetal force is the force that keeps an object moving in a circular path. It is always directed towards the center of the circle and is responsible for changing the direction of the object's velocity. Without centripetal force, the object would continue to move in a straight line.

How is circular motion related to Newton's laws of motion?

Circular motion is related to Newton's laws of motion in several ways. The first law states that an object will continue to move in a straight line at a constant velocity unless acted upon by an external force. In circular motion, the centripetal force acts as the external force that changes the object's direction. The second law states that the force applied to an object is directly proportional to its mass and acceleration. In circular motion, the centripetal force is proportional to the mass of the object and the square of its velocity, resulting in a constant acceleration towards the center of the circle. Finally, the third law states that for every action, there is an equal and opposite reaction. In circular motion, the centripetal force is countered by the centrifugal force, which is the force pushing the object outwards.

What is the difference between uniform circular motion and non-uniform circular motion?

Uniform circular motion is when an object moves along a circular path at a constant speed. In this type of motion, the object's velocity is always perpendicular to its position, resulting in a constant radius of curvature. Non-uniform circular motion is when an object moves along a circular path at varying speeds. In this type of motion, the object's velocity is not always perpendicular to its position, resulting in a changing radius of curvature.

What are some real-life examples of circular motion?

Some common examples of circular motion in everyday life include the Earth's orbit around the sun, a car turning a corner, a spinning top, and a rollercoaster loop. Other examples include the motion of planets and moons in our solar system, the movement of a tetherball around a pole, and the rotation of a ceiling fan.

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