Calculating Final Angular Speed of a Rotating Disk with a Horizontal Axis

In summary: There are three laws that are commonly associated with angular motion: conservation of angular momentum, conservation of linear momentum, and conservation of energy.
  • #1
ooohffff
74
1

Homework Statement


You connect a light string to a point on the edge of a uniform vertical disk with radius R and mass M. The disk is free to rotate without friction about a stationary horizontal axis through its center. Initially, the disk is at rest with the string connection at the highest point on the disk. You pull the string with a constant horizontal force F⃗ until the wheel has made exactly one-quarter revolution about a horizontal axis through its center, and then let go.

Find the final angular speed of the disk.

Homework Equations


v=r(omega)

The Attempt at a Solution



Not totally sure where to start?
 
Physics news on Phys.org
  • #2
Do you know the answer to this problem? If so, can you post it?
 
  • #3
As you have a constant force (F) and no friction, the disk will ... (?)
Now write the equations you know for (?)
Hth :)
 
  • #4
The simplest type of angular motion problems have a constant torque, which results in a constant angular acceleration. In your problem, unless I am reading it wrong, the force is constant but the perpendicular distance to the axis of rotation is not constant. (The reason the perpendicular distance is not constant is because the point where the force is applied is rotating with the disk, but the direction of the force is not rotating with the disk - because it is specified in the problem that it is a constant HORIZONTAL force.) The result is an angular acceleration that is NOT constant. Any idea how you can find angular velocity from a varying angular acceleration?
 
  • Like
Likes billy_joule
  • #5
Replusz said:
As you have a constant force (F) and no friction, the disk will ... (?)
Now write the equations you know for (?)
Hth :)
Not sure where you were headed with that. If you were thinking in terms of linear forces and accelerations, there is also a non-constant force. If you were thinking in terms of torques and angular accelerations, as TomHart points out, the torque is not constant.
 
  • #6
TomHart said:
Do you know the answer to this problem? If so, can you post it?
No, I do not know the answer.
 
  • #7
ooohffff said:

Homework Equations

Any conservation laws that might apply?
 
  • #8
haruspex said:
Any conservation laws that might apply?

Conservation of angular momentum?
 
  • #9
ooohffff said:
Conservation of angular momentum?
What conditions do you need to be able to apply that? What reference point would you take as axis?
Any other laws?
 

1. What is angular speed and how is it different from linear speed?

Angular speed is a measure of how quickly an object rotates around a fixed point. It is different from linear speed, which measures how quickly an object moves in a straight line. Angular speed is measured in radians per second, while linear speed is measured in meters per second.

2. How do you calculate the angular speed of a disk?

The formula for calculating angular speed is ω = θ/t, where ω is the angular speed in radians per second, θ is the angular displacement in radians, and t is the time in seconds. For a disk, θ is equal to the circumference of the disk, and t is the time it takes for the disk to make one full revolution.

3. Can you explain the relationship between angular speed and rotational speed?

Angular speed and rotational speed are directly proportional. This means that as the angular speed increases, the rotational speed also increases. This relationship is described by the equation v = ωr, where v is the rotational speed, ω is the angular speed, and r is the radius of the disk.

4. How can you measure the angular speed of a disk?

The angular speed of a disk can be measured using a tachometer, which is a device that measures the number of revolutions per unit of time. Alternatively, it can also be measured by recording the time it takes for the disk to make one full rotation and using the formula ω = θ/t.

5. What factors can affect the angular speed of a disk?

The angular speed of a disk can be affected by several factors, including the mass and shape of the disk, the amount of friction and resistance present, and the force or torque applied to the disk. Changes in any of these factors can result in a change in the angular speed of the disk.

Similar threads

Determining $L_{o}$: Finding Angular Momentum of System
    • Introductory Physics Homework Help
2
Replies
45
Views
2K
Perfectly inelastic collision of two moving and rotating disks
    • Introductory Physics Homework Help
Replies
9
Views
1K
Conservation of Energy and Angular Momentum in a Rotating Train-Disk System
    • Introductory Physics Homework Help
Replies
30
Views
2K
What is the Angular Velocity Acquired by a Disk on a Rotating Platform?
    • Introductory Physics Homework Help
Replies
28
Views
3K
Angular speed calculation after an inelastic collision
    • Introductory Physics Homework Help
Replies
20
Views
2K
Angular momentum after a collision
    • Introductory Physics Homework Help
Replies
1
Views
1K
Why Do Moments Balance in a Faraday Disk but Not the Forces?
    • Introductory Physics Homework Help
Replies
1
Views
764
Determining the Speed of a Rotating Disk with a Constant Force
    • Introductory Physics Homework Help
Replies
10
Views
2K
Why did I get this angular momentum problem wrong?
    • Introductory Physics Homework Help
Replies
25
Views
9K
Time required for disk to reach angular speed?
    • Introductory Physics Homework Help
Replies
11
Views
2K

Hot Threads

Recent Insights

Back
Top