Problem with average velocity in a circle

In summary, the problem involves a particle moving with constant speed in a circle with a radius of 7.4 m, completing one revolution in 22.0 s. The magnitude of the average velocity during the interval from t = 4.4 s to t = 18.7 s is being sought, but the answer using the formula for velocity was rejected. This is because the speed in a circle is constant, not the velocity. The correct approach is to find the net displacement of the particle and divide it by the time to get the average velocity.
  • #1
DuffBeer
6
0
A particle P travels with constant speed in a circle of radius 7.4 m and completes one revolution in 22.0 s (see Figure). The particle passes through O at t = 0 s. What is the magnitude of the average velocity during the interval from t = 4.4 s and t = 18.7 s.

I used T=2(pi)r / v

22 = 2*pi*7.4/v
v = 2.11 m/s

But the answer was rejected... The velocity in a circle is supposed to be constant, why won't my answer work?
 
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  • #2
DuffBeer said:
But the answer was rejected... The velocity in a circle is supposed to be constant, why won't my answer work?
The speed is constant, not the velocity.
 
  • #3
Doc Al said:
The speed is constant, not the velocity.

Oh man... Does that mean my answer is just negative since it's moving counterclockwise?
 
  • #4
find the displacement

DuffBeer said:
Oh man... Does that mean my answer is just negative since it's moving counterclockwise?
No. I suspect they want you to find the net displacement of the particle from t = 4.4 s to t = 18.7 s. Find out where it is on the circle at those two points, and then figure the displacement. The "average velocity" will be the net displacement divided by the time.
 

FAQ: Problem with average velocity in a circle

What is the definition of average velocity in a circle?

The average velocity in a circle is the average rate of change of position around the circumference of the circle. It is a vector quantity that takes into account both the magnitude and direction of the motion.

How is average velocity in a circle different from linear average velocity?

While linear average velocity only considers the distance traveled in a straight line, average velocity in a circle takes into account the change in direction as well. This means that even if an object travels the same distance in a circle, its average velocity will be different depending on the radius and angle of the circle.

How is average velocity in a circle calculated?

To calculate average velocity in a circle, you must divide the total distance traveled around the circumference of the circle by the total time taken. This will give you the average speed. To determine the average velocity, you must also consider the direction of the motion and calculate the change in angle over the same time period.

Can the average velocity in a circle be negative?

Yes, the average velocity in a circle can be negative. This occurs when the direction of motion is opposite to the direction of rotation around the circle. For example, if an object travels clockwise around a circle, but its overall direction of motion is counterclockwise, its average velocity will be negative.

Why is average velocity in a circle important in physics?

Average velocity in a circle is important in physics because it helps us understand the motion and behavior of objects in circular motion. It is also used in many real-world applications, such as calculating the average speed of a race car around a circular track or determining the average velocity of planets in orbit around the sun.

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