Finding the position vector of uniform circular motion

In summary, to find the position of an object moving in a circle, you can use the equations x = rcos(wt) and y = rsin(wt) where w is the angular velocity and r is the radius of the circle. To find the velocity of the object, you can use the equations dx/dt = -rwsin(wt) and dy/dt = rwcos(wt).
  • #1
LavastormSW
1
0

Homework Statement



Write an equation for one component of the position vector as a function of the radius of the circle and the angle the vector makes with one axis of your coordinate system. Calculate how that angle depends on time and the constant angular speed of the object moving in a circle.

Homework Equations



a = v2 / r
D = 2∏r
v = D / t

The Attempt at a Solution



I really don't know where to begin. The lab book says to look at an equation in the textbook that doesn't exist, or, if it does, that I can't find.
 
Last edited:
Physics news on Phys.org
  • #2
x = rcos(wt)
y = rsin(wt)

for position where w is the angular velocity

if r is constant

dx/dt = -rwsin(wt)
dy/dt = rwcos(wt)
 

1. What is the position vector of uniform circular motion?

The position vector of uniform circular motion is a vector that starts from the center of the circle and points to any point on the circle. It represents the location of the object at a specific time during its circular motion.

2. How do you find the position vector of uniform circular motion?

To find the position vector of uniform circular motion, you need to know the radius of the circle, the angular velocity, and the time. You can then use the formula r = R(cosθ, sinθ) to calculate the x and y components of the position vector, where R is the radius, θ is the angular position, and r is the magnitude of the position vector.

3. What is the difference between position vector and displacement vector in uniform circular motion?

The position vector represents the location of the object at a specific time during its circular motion, while the displacement vector represents the change in position from the initial to final position. The position vector is a continuous vector, while the displacement vector is a single vector that connects the initial and final positions.

4. Can the position vector of uniform circular motion change in magnitude?

No, the position vector of uniform circular motion does not change in magnitude. It always has the same length, which is equal to the radius of the circle. However, its direction changes as the object moves along the circular path.

5. How does the position vector of uniform circular motion relate to the velocity vector?

The position vector and the velocity vector are perpendicular to each other in uniform circular motion. The velocity vector is tangent to the circle at any given point, while the position vector is always perpendicular to the velocity vector. This means that the position vector and the velocity vector have a constant angle between them, which is equal to 90 degrees.

Similar threads

Acceleration in uniform circular motion is uniform or non-uniform?
    • Introductory Physics Homework Help
2
Replies
55
Views
656
Kinematics, curvilinear motion (a couple of questions)
    • Introductory Physics Homework Help
Replies
30
Views
500
Deviation of Plumb Bob In Uniform Circular Motion
    • Introductory Physics Homework Help
Replies
11
Views
2K
A Car on a Banked Curve Moving in Uniform Circular Motion
    • Introductory Physics Homework Help
Replies
7
Views
2K
Position vector for anti-clockwise circular motion derivation
    • Introductory Physics Homework Help
Replies
5
Views
587
Find the acceleration in circular motion
    • Introductory Physics Homework Help
Replies
6
Views
963
Trouble understanding vector hat notation - Circular Motion
    • Introductory Physics Homework Help
Replies
7
Views
2K
Circular Motion Problem: Particle Velocity and Acceleration Calculation
    • Introductory Physics Homework Help
Replies
18
Views
2K
The components of force and velocity vectors in circular motion
    • Introductory Physics Homework Help
Replies
11
Views
2K
Circular motion of a mass on a string on an inclined plane
    • Introductory Physics Homework Help
Replies
14
Views
2K

Hot Threads

Recent Insights

Back
Top