Location of an object moving in a circular path

In summary, to find the location of an object with Cartesian coordinates (x,y) based on its speed and radius of turn, you can use parametric equations x=r cos (\alpha) and y=r sin (\alpha) where \alpha is the angle in radians and r is the radius. By calculating the distance traveled based on the speed and time, you can then find \alpha in terms of your normal time variable and use it to determine the object's location.
  • #1
vbman11
5
0
if i know the speed and the radius of the turn how can I find the location of the object(x,y Cartesian) of the object with Time?
 
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  • #2
You could describe the circle parametrically as:
[tex] x=r cos (\alpha)[/tex]
[tex] y=r sin (\alpha)[/tex]

Then, knowing v, you can find the period it should take for the object to complete one revolution and compute alpha in terms of your normal time variable.
 
  • #3
ok so, I am guessing [tex]\alpha[/tex] is the angle in radians and r is the radius. so I use the speed(s) and time(t) to get the distance then divide that by the circumference then multiply by 2[tex]\pi[/tex] to get the radians to put into those equations?
 

What is circular motion?

Circular motion is the movement of an object along a circular path. It occurs when an object has a constant speed and direction, but its direction is continuously changing.

What is the difference between linear and circular motion?

Linear motion is when an object moves in a straight line, while circular motion is when an object moves in a circular path. In linear motion, the object's speed and direction remain constant, while in circular motion, the object's speed remains constant but its direction changes.

What is the centripetal force in circular motion?

The centripetal force is the force that keeps an object moving in a circular path. It acts towards the center of the circle and is necessary to maintain the object's constant speed and direction in circular motion.

How is the velocity of an object in circular motion calculated?

The velocity of an object in circular motion can be calculated by dividing the circumference of the circle by the time it takes to complete one full revolution. This is known as the tangential velocity.

What is the relationship between the radius of a circle and the speed of an object in circular motion?

The speed of an object in circular motion is directly proportional to the radius of the circle. This means that as the radius increases, the speed of the object also increases, and vice versa.

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