How Does Angular Velocity Affect Circular Motion?

In summary: So, if an observer is located at the North Pole and sees the object rotating around the z-axis, the angular velocity would be positive (toward the observer) and the direction of the angular velocity would be in the direction of the arrow on the xy plane.
  • #1
TheNormalForc
12
0
1. For an object in circular motion, which of the following is/are directed perpendicular to the plane of the circle?

Angular Acceleration, Tengintial Velocity, Angular Velocity, Tangential Acceleration, or Angular Displacement?

2. You are on Earth. Assume that one month is about 30 days and that the moon is about 60 times as far from the center of the circular Earth as you are. Then the tanginitial speed of the moon in its orbit (assumed circular) around the Earth is about

Equal to your tengential speed, 60 times your tangintial speed, twice your tangential speed, or half your tangintial speed?




Homework Equations



S=r(theta)
v=r(omega)
a=r(alpha)



The Attempt at a Solution



They're not really matamaticas problems, but test of concept; which I don't really seem to have a grasp of.

Beyond those, there a few matmatical stumpers.

Assume that the equitorial radius of the Earth is 6.4x10^6 m and that the length of a day at the equator is 24 hours. You are standing on the equator of the rotating Earth.

1. What is the period of your uniform circular motion in seconds?


I calculated 1/86400 cycles per second.

2. What is the frequency of your circular motion in Hertz?

3. What is the magnitude of your angular acceleration in rad/s^2

4. What is your tangential speed in m/s

5. The plane of your circular motion is certainly the equitorial plane. If an observer in a spaceship high above the pole correctly states that your angular velocity vector is directed toward her, then the spaceship is above which pole? Explain.


I could calculate the acceleration and speed if I was given a slight hint, but the frequency and "poles" question leave me baffaled.

Ok, I calculated the tingential speed to be 465 m/s, and the angular acceleration to be 0. Still need help on the proof of concept, the frequency, and poles questions though.
 
Last edited:
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  • #2
Whenever you have a vector described using a direction of rotation, it always points perpendicular to the plane in which the rotation is taking place. Also, it would be good to note that angular displacement is not a vector quantity.
 
  • #3
TheNormalForc said:
2. What is the frequency of your circular motion in Hertz?

3. What is the magnitude of your angular acceleration in rad/s^2

4. What is your tangential speed in m/s

5. The plane of your circular motion is certainly the equitorial plane. If an observer in a spaceship high above the pole correctly states that your angular velocity vector is directed toward her, then the spaceship is above which pole? Explain.


I could calculate the acceleration and speed if I was given a slight hint, but the frequency and "poles" question leave me baffaled.

Ok, I calculated the tingential speed to be 465 m/s, and the angular acceleration to be 0. Still need help on the proof of concept, the frequency, and poles questions though.

Frequency is the number of times something happens per unit time. If the period of rotation is T, what would be the frequency? Think for a while.

The angular velocity is considered positive toward the z-axis when something rotates on the xy plane counter clockwise when seen from the direction of the z-axis.
 

Related to How Does Angular Velocity Affect Circular Motion?

1. What is angular velocity?

Angular velocity is a measure of how quickly an object is rotating around a specific axis. It is usually represented by the symbol "ω" and is measured in radians per second (rad/s).

2. How is angular velocity different from linear velocity?

Angular velocity is a vector quantity that measures the rate of rotation, while linear velocity is a vector quantity that measures the rate of change in position. Angular velocity is dependent on the axis of rotation, while linear velocity is not.

3. What is the formula for calculating angular velocity?

The formula for angular velocity is ω = Δθ/Δt, where ω is angular velocity, Δθ is the change in angle in radians, and Δt is the change in time.

4. How does angular velocity relate to centripetal acceleration?

Angular velocity and centripetal acceleration are related through the formula a = ω²r, where a is the centripetal acceleration, ω is the angular velocity, and r is the distance from the object to the axis of rotation. This means that the greater the angular velocity, the greater the centripetal acceleration.

5. How is angular velocity used in real life?

Angular velocity is used in many real-life applications, such as engineering, physics, and sports. For example, it is used to calculate the speed and trajectory of a spinning ball in sports such as baseball and tennis. In engineering, it is used to design and optimize rotating machinery. In physics, it is used to study the motion of planets and other celestial bodies.

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