Rotational Motion of a toy airplane

In summary, the problem involves an airplane flying in a circular motion on a string and the given information includes the tension of the string (6.5N) and the angle of flight (50°). The task is to find the angular velocity, mass of the plane, and length of the string. Using the equation ω=2π(period), the angular velocity is calculated to be 5.28 m/s with a period of 1.19s/rev. By using Newton's 2nd law and equating the force of gravity to the y-component of the tension force, the mass of the plane is found to be 0.42 kg. To find the length of the string, the radius of the circular motion
  • #1
SChiO
11
0

Homework Statement



We were given a video...I'm not sure if you can post video links otherwise I would...but it's a video of an airplane on a string flying in a circular motion. On the top of the string you can see that the tension of the string is 6.5N. and it is flying at an angle of 50°. We are told to find the angular velocity, mass of plane and length of string.


The Attempt at a Solution



Using ω=2pi(period) I found it to be 5.28 m/s with a period of 1.19s/rev
Using Newton's 2nd law and knowing that the force of gravity is equal to the y-component of the tension force I found the mass to be equal to .42 kg.
However I am stuck on finding the length of the string...I have an idea that I need to find the radius of the circle and then from there I know I can find the length of the string but I'm not sure how to find the radius. I'm thinking to use this equation: v=rω but I'm not sure how to find the linear velocity or if that's even right...HELP PLEASE! I'll see if I can post the video for ease...Thanks
 
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  • #2
SChiO said:

Homework Statement



We were given a video...I'm not sure if you can post video links otherwise I would...but it's a video of an airplane on a string flying in a circular motion. On the top of the string you can see that the tension of the string is 6.5N. and it is flying at an angle of 50°. We are told to find the angular velocity, mass of plane and length of string.
You can post links to a video - but it is best to give a written description anyway.
Is that 50deg angle to the horizontal or the vertical?
Using ω=2pi(period) I found it to be 5.28 m/s with a period of 1.19s/rev
Just a note - the units of ##\omega## is radiens per second. Since you were "given the angular velocity" I'm guessing you mean that the tangential velocity was 5.28m/s.
"Period" is usually just given in seconds.

Using Newton's 2nd law and knowing that the force of gravity is equal to the y-component of the tension force I found the mass to be equal to .42 kg.

However I am stuck on finding the length of the string...I have an idea that I need to find the radius of the circle and then from there I know I can find the length of the string but I'm not sure how to find the radius.
Hint: centripetal force and acceleration.
 

1. What is rotational motion?

Rotational motion is the movement of an object around an axis or center point. In the case of a toy airplane, it refers to the spinning motion of the propeller as it flies through the air.

2. How does rotational motion affect the flight of a toy airplane?

Rotational motion plays a crucial role in the flight of a toy airplane. The spinning propeller creates thrust, which propels the airplane forward. It also helps to stabilize the airplane by keeping it level and preventing it from tipping to one side.

3. What factors can impact the rotational motion of a toy airplane?

The rotational motion of a toy airplane can be affected by several factors, such as the speed of the propeller, the weight and balance of the airplane, and external forces such as wind or turbulence. Additionally, the design and quality of the propeller can also impact its rotational motion.

4. How does the rotational motion of a toy airplane differ from that of a real airplane?

The rotational motion of a toy airplane is typically simpler and more limited compared to that of a real airplane. Toy airplanes often have a single propeller that spins in only one direction, while real airplanes may have multiple engines and more complex rotational movements. Real airplanes also have advanced control systems to manipulate and adjust their rotational motion as needed for different flight maneuvers.

5. Can the rotational motion of a toy airplane be changed or controlled?

Yes, the rotational motion of a toy airplane can be changed or controlled to a certain extent. By adjusting the speed of the propeller or altering the weight and balance of the airplane, you can impact its rotational motion. Some toy airplanes also come with remote controls that allow you to change the direction and speed of the propeller, giving you more control over its rotational motion during flight.

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