How Does Increasing Rotation Frequency Affect Centripetal Force?

Click For Summary

Homework Help Overview

The discussion revolves around concepts of circular motion, specifically focusing on centripetal force, centripetal acceleration, and the speed of satellites in orbit. Participants are exploring how changes in rotation frequency affect centripetal force, as well as calculating various parameters related to circular motion.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants are attempting to relate centripetal force to frequency of rotation and questioning how these concepts interact. There are inquiries about the gravitational forces acting on satellites and how to derive the necessary equations for calculations. Some participants express confusion regarding specific terms and concepts, such as gravitational force and its relation to centripetal force.

Discussion Status

Several participants have provided calculations and attempted to clarify their understanding of the relationships between the variables involved. Some guidance has been offered regarding the equations needed, but there remains a lack of consensus on certain concepts, particularly around gravitational forces and their application to the problems presented.

Contextual Notes

Participants have noted that some are struggling with the material due to missed classes, which may affect their understanding of the topic. There are references to external resources, such as Wikipedia, for additional context, but no resolution to the confusion surrounding specific equations and concepts has been reached.

SHENGTON
Messages
6
Reaction score
0
Hello guys, good morning. :)

I need your help regarding Circular Motion. I'm hoping that someone will help me heartily with this.

These are the following problems:
1. When the radius and mass are held constant, what do you expect to happen to the centripetal force if the frequency of rotation is increased?

2. Determine the speed of the satellite orbiting at a height of 700km above the Earth's surface.

mass of Earth = 5.98 x 10^24kg
radius of Earth = 6.38 x 10^6m

3. How much centripetal acceleration is produced when the object rotates 40 times a second with 4.89m radius? Also compute for the tangential velocity.

That's all guys. Hope you can help me with these. Thanks advance.
 
Physics news on Phys.org
SHENGTON said:
Hello guys, good morning. :)

I need your help regarding Circular Motion. I'm hoping that someone will help me heartily with this.

These are the following problems:
1. When the radius and mass are held constant, what do you expect to happen to the centripetal force if the frequency of rotation is increased?

2. Determine the speed of the satellite orbiting at a height of 700km above the Earth's surface.

mass of Earth = 5.98 x 10^24kg
radius of Earth = 6.38 x 10^6m

3. How much centripetal acceleration is produced when the object rotates 40 times a second with 4.89m radius? Also compute for the tangential velocity.

That's all guys. Hope you can help me with these. Thanks advance.

What are your attempts on the questions? What equations do you need to use?

For the first one, how does centripetal force relate to the frequency of rotation?

For the second one, what is providing the centripetal force needed to keep the satellite in orbit?
 
Hello rock.freak667, good morning. :)

Thanks for replying my post Sir. Actually, I really don't know Sir. I don't know how will I answer you questions about my homework. Because I'm kinda late with this topic because I'm on the tour when they discussed this. I'm a 3rd year student and my classmates are 1st year. So it's a bit favor with them because I'm on the tour with my other 3rd year batch here in the Philippines.
 
SHENGTON said:
Hello rock.freak667, good morning. :)

Thanks for replying my post Sir. Actually, I really don't know Sir. I don't know how will I answer you questions about my homework. Because I'm kinda late with this topic because I'm on the tour when they discussed this. I'm a 3rd year student and my classmates are 1st year. So it's a bit favor with them because I'm on the tour with my other 3rd year batch here in the Philippines.

Wikipedia explains it well

Read it, see if you can grasp the concepts and are able to get started on the questions

http://en.wikipedia.org/wiki/Uniform_circular_motion"
 
Last edited by a moderator:
Hello rock.freak667.

Thanks again for replying my post. Here's what I got:

1. When the radius and mass are held constant, what do you expect to happen to the centripetal force if the frequency of rotation is increased?

Answer:
The centripetal force will also increase (force = m x (v^2/radius))

2. Determine the speed of the satellite orbiting at a height of 700km above the Earth's surface. The mass of Earth is 5.98 x 10^24kg and the radius of Earth is 6.38 x 10^6m.

Answer:
g(h)=g(0)*(R/(R+h))^2 where g(0)=9.81
g(700)=7.966
v=radical(rg)=7510 m/s

3. How much centripetal acceleration is produced when the object rotates 40 times a second with 4.89m radius? Also compute for the tangential velocity.

Answer:
Compute for Tangential Velocity:
Tangential Velocity = frequency x 2pi x radius
Tangential Velocity = 40 x 2pi x 4.89 = 251.327
Tangential Velocity = 251.327 x 4.89 = 1228.99 m/s

Compute for Centripetal Acceleration:
Centripetal Acceleration = tangential velocity^2 / radius
Centripetal Acceleration = 1228.99 m/s^2 / 4.89
Centripetal Acceleration = 308878.6135 m/s^2 or 308879 m/s^2


I think number 1 and 3 are already OK. But I'm bit confuse with number 2 (red color). I just copy the answer of number 2 from Yahoo Answers. I don't understand what is g(0), R, and h. What are these? Hope you can help me with this.

Thanks advance.
 
SHENGTON said:
Hello rock.freak667.

Thanks again for replying my post. Here's what I got:

1. When the radius and mass are held constant, what do you expect to happen to the centripetal force if the frequency of rotation is increased?

Answer:
The centripetal force will also increase (force = m x (v^2/radius))

While this answer is correct, the asked for the frequency of rotation ω, so remember that v=rω, so put that back into your equation for centripetal force.

SHENGTON said:
2. Determine the speed of the satellite orbiting at a height of 700km above the Earth's surface. The mass of Earth is 5.98 x 10^24kg and the radius of Earth is 6.38 x 10^6m.

Answer:
g(h)=g(0)*(R/(R+h))^2 where g(0)=9.81
g(700)=7.966
v=radical(rg)=7510 m/s

Do you know Newton's law of gravitation? If you do, the gravitational force between the Earth and the satellite provides the centripetal force such that

Fgravitational=Fcentripetal

What is the gravitational force between the Earth and the satellite.

SHENGTON said:
3. How much centripetal acceleration is produced when the object rotates 40 times a second with 4.89m radius? Also compute for the tangential velocity.

Answer:
Compute for Tangential Velocity:
Tangential Velocity = frequency x 2pi x radius
Tangential Velocity = 40 x 2pi x 4.89 = 251.327
Tangential Velocity = 251.327 x 4.89 = 1228.99 m/s

Compute for Centripetal Acceleration:
Centripetal Acceleration = tangential velocity^2 / radius
Centripetal Acceleration = 1228.99 m/s^2 / 4.89
Centripetal Acceleration = 308878.6135 m/s^2 or 308879 m/s^2

this looks correct to me.
 
I don't know about the Newton's Law of Gravitation. Can you help me solve with this?
 
SHENGTON said:
I don't know about the Newton's Law of Gravitation. Can you help me solve with this?

The gravitational force between two point masses M and m separated by a distance r is given by

F= \frac{GMm}{r^2}


Where G is the universal gravitational constant 6.67x10-11 Nm2/kg2
 
Here's my answer in number 2. Kindly check if the equation is correct.

Answer:
The force on the satellite due to the Earth is given by:
F = G(me * ms)/r^2

me = 5.98 x10^24 kg = 5,980,000,000,000,000,000,000,000kg
ms = mass of satellite
G = Gravitational Constant = 6.67 x 10^-11 N(m/kg)^2 = 0.0000000000667 N(m/kg)^2
r = 6.38 x10^6m + 700km x 1000m / 1km = 7,080,000m

Object moving in a circular motion will have force given by:
F = (ms * v^2)/r

Equating the equations:
“G(me*ms)/r^2 = (ms*v^2)/r” to “v = square root (G*me/r)”

V = sqrt (0.0000000000667N(m/kg)^2 x 5,980,000,000,000,000,000,000,000kg / 7,080,000m)
V = sqrt (56337005.64971751412429)
V = 7505.79813542287547472866
V = 7505.80m/s
 

Similar threads

How does radius affect frequency in uniform circular motion?
  • · Replies 17 ·
Replies
17
Views
9K
Circular Motion Questions (energies, forces, angular velocities, etc.)
  • · Replies 2 ·
Replies
2
Views
2K
Centripetal Force and circular motion
  • · Replies 3 ·
Replies
3
Views
2K
When do I include the Earth's radius in questions involving satellites?
  • · Replies 5 ·
Replies
5
Views
3K
Circular motion/ speed increases at a constant rate
  • · Replies 7 ·
Replies
7
Views
2K
Centripetal Force / circular motion question
  • · Replies 7 ·
Replies
7
Views
4K
Circular Motion of a Cyclist and a Car going around a bend in the road
  • · Replies 6 ·
Replies
6
Views
4K
The components of force and velocity vectors in circular motion
  • · Replies 11 ·
Replies
11
Views
3K
Question Regarding Circular Motion and Normal Forces
  • · Replies 2 ·
Replies
2
Views
3K
Calculating Tidal Range (Gravitation)
  • · Replies 12 ·
Replies
12
Views
3K