Circular Motion with Vector Notation

[apphysics11]

Homework Statement

A particle is in uniform circular motion about the origin of an xy coordinate system, moving clockwise with a period of 7.00 s. At one instant, its position vector (from the origin) is r = (6.00 m) i - (3.00 m) j. At that instant, what is its velocity in unit-vector notation?

Homework Equations

V=2pir/T

The Attempt at a Solution

I know to find the radius, you can use pythag which i got as 6.70m. but i don't know where to go from here. since if i just use the circular velocity equation i don't know how to put it back into unit-vector. also i haven't been taught angular motion which i have seen been used to solve it.

thanks.

 

[anathema]

Thank you for your post. To find the velocity in unit-vector notation, you can use the formula v = rω, where r is the radius and ω is the angular velocity. In this case, the angular velocity can be found by using the formula ω = 2π/T, where T is the period. Plugging in the values given in the problem, we get ω = 2π/7.00 s = 0.897 rad/s.

Now, to find the velocity in unit-vector notation, we need to find the components of the velocity vector in the i and j directions. We can do this by using the formula v = rω = (6.70 m)(0.897 rad/s) = 6.00 m/s. This is the magnitude of the velocity vector.

To find the components, we can use trigonometric functions. The x-component of the velocity vector can be found using the formula vx = vcosθ, where θ is the angle between the velocity vector and the x-axis. In this case, θ = 90° since the particle is moving clockwise. Therefore, vx = (6.00 m/s)cos90° = 0 m/s.

Similarly, the y-component of the velocity vector can be found using the formula vy = vsinθ, where θ is the angle between the velocity vector and the y-axis. In this case, θ = 180° since the particle is moving clockwise. Therefore, vy = (6.00 m/s)sin180° = -6.00 m/s.

Putting these components together, we get the velocity vector in unit-vector notation as v = (0 m/s) i + (-6.00 m/s) j.

I hope this helps. Let me know if you have any further questions.



Scientist