Circular Motion with Vector Notation

In summary, to find the velocity in unit-vector notation for a particle in uniform circular motion, you can use the formula v = rω, where r is the radius and ω is the angular velocity. The angular velocity can be found using the formula ω = 2π/T, where T is the period. To find the components of the velocity vector, you can use trigonometric functions. In this case, the velocity vector is v = (0 m/s) i + (-6.00 m/s) j.
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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.
 
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  • #2


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.



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FAQ: Circular Motion with Vector Notation

1. What is circular motion with vector notation?

Circular motion with vector notation is a method of representing circular motion using vectors, which are mathematical quantities that have both magnitude and direction. It allows for a more precise and visual understanding of the motion of an object in a circular path.

2. How is circular motion with vector notation different from regular circular motion?

In regular circular motion, the motion is described using scalar quantities such as speed and distance. However, in circular motion with vector notation, the motion is described using vector quantities such as velocity and acceleration, which take into account the direction of the motion.

3. What are the key components of circular motion with vector notation?

The key components of circular motion with vector notation are the radius of the circular path, the angular velocity (how fast the object is rotating), and the tangential velocity (the speed of the object along the circular path).

4. How does vector notation help us understand circular motion better?

Vector notation allows us to break down the motion of an object in a circular path into its components, such as the tangential and radial components. This helps us to analyze the motion more precisely and understand the effects of different forces on the object.

5. What are some real-life examples of circular motion with vector notation?

Some common examples of circular motion with vector notation include the motion of a satellite in orbit around a planet, the rotation of a Ferris wheel, and the motion of a car around a circular track. It can also be applied to the motion of planets around the sun and the rotation of the Earth on its axis.

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