Average velocity vector of non-uniform circular motion?

In summary, a particle starting from rest revolved with uniformly increasing speed in a clockwise circle in an xy plane. At t=0, the particle was at x=0.0m, y=2.0m. At t=2.0s, it had made one-quarter of a revolution and was at x=2.0m, y=0.0m. The speed at t=2.0s was π/2 m/s, the average velocity vector was (π/2, -1) m/s, and the average acceleration vector during this interval was (√2π/4, -π/4) m/s². To calculate these values, the equations used were a_R = v
  • #1
Carpetfizz
13
0

Homework Statement


A particle starting from rest revolves with uniformly increasing speed in a clockwise circle in an xy plane. The center of the circle is at the origin of an xy coordinate system. At t=0, the particle is at x=0.0m, y=2.0m. At t=2.0s, it has made one-quarter of a revolution and is at x=2.0m,y=0.0m.

(a) Speed at t=2.0s?
(b) Average velocity vector?
(c) Average acceleration vector during this interval.

Homework Equations



$$a_{tan} = \frac{dv}{dt}$$
$$a_R = \frac{v^2}{r}$$
$$a = \sqrt{a^2_{tan}+a^2_{R}}$$

The Attempt at a Solution



a)
$$r = 2$$
$$d = \frac{2 \pi (2)}{4} = \pi$$
$$v = \frac{\pi}{2}$$

b, c) I don't know where to start because it's asking for a vector which implies that we need to calculate the "average angle" ?
 
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  • #2
Your answer for a) is wrong. what equations do you know for uniform acceleration? (Usually called the SUVAT equations.)
Also, you should state the units in the answers.
 

1. What is non-uniform circular motion?

Non-uniform circular motion is the motion of an object moving along a circular path at a varying speed. This means that the object's velocity, or speed and direction, changes at different points along the path.

2. How do you calculate average velocity vector in non-uniform circular motion?

To calculate the average velocity vector in non-uniform circular motion, you need to find the displacement vector, or the change in position, divided by the time interval. This will give you the average velocity vector, which takes into account both the magnitude and direction of the object's motion.

3. What factors can affect the average velocity vector in non-uniform circular motion?

The average velocity vector in non-uniform circular motion can be affected by the object's acceleration, the shape and size of the circular path, and any external forces acting on the object. These factors can cause the object's velocity to change, resulting in a different average velocity vector.

4. How does the average velocity vector differ from the instantaneous velocity vector in non-uniform circular motion?

The average velocity vector represents the overall motion of an object over a certain time interval, while the instantaneous velocity vector represents the object's velocity at a specific moment in time. In non-uniform circular motion, the instantaneous velocity vector may be different at different points along the circular path, while the average velocity vector takes into account all of these changes.

5. Can the average velocity vector in non-uniform circular motion be negative?

Yes, the average velocity vector in non-uniform circular motion can be negative if the object's motion is in the opposite direction of the chosen coordinate system. This means that the object is moving in a clockwise direction, while the coordinate system measures motion in the counterclockwise direction, resulting in a negative average velocity vector.

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