# Determining the Speed of a Rotating Disk with a Constant Force

• Kenneth Dirk
In summary: Quite so, but it is also important that the student come to understand why the attempted method went wrong.
Kenneth Dirk

## Homework Statement

A solid uniform disk of mass 21.0 kg and radius 85.0 cm is at rest flat on a frictionless surface A string is wrapped around the rim of the disk and a constant force of 35.0 N is applied to the string. The string does not slip on the rim.
1- When the disk has moved a distance of 5.5 m, determine how fast it is moving.

## Homework Equations

Kinetic energy= (mv^2)/2 Rotational kinetic energy = (Iw^2)/2 Work=Fdcos(theta)
I(disk)=(mr^2)/2

## The Attempt at a Solution

Since the object is at rest, I know that the initial kinetic energy of the disk is zero and that after applying a force it will have final kinetic energy both rotation and translation.
So my energy of conservation equation would be
Work done by pulling= Kinetic energy Translational + Kinetic energy Rotational
(35)(5.5) = v^2( (m/2) + (m/4)
When I solve for v, I get 3.49. But the answer is 4.3 m/s. Is my conservation of energy equation wrong?

Yes.

BvU said:
Yes.
What is wrong with the equation? Could you please guide me?

Kenneth Dirk said:
What is wrong with the equation? Could you please guide me?
Note you used "v" and "w" in your relevant equations. Did you think they are the same?

To start with, your calculation of the work done is incorrect. (Reconsider the distance over which the applied force acts.)

perot said:
Note you used "v" and "w" in your relevant equations. Did you think they are the same?
No. I wrote the w in terms of v. Isn't that correct?

Doc Al said:
To start with, your calculation of the work done is incorrect. (Reconsider the distance over which the applied force acts.)
Doesn't the pulling force cause the disk to move a distance of 5.5m? So wouldn't the work formula include 5.5m? I am confused. Could you please elaborate.

Kenneth Dirk said:
Doesn't the pulling force cause the disk to move a distance of 5.5m?
True.

Kenneth Dirk said:
So wouldn't the work formula include 5.5m?
Realize that the point of application of the force is on the string. Imagine you are pulling that string. How far will you have to pull it to meet the conditions of this problem?

Doc Al said:
True.Realize that the point of application of the force is on the string. Imagine you are pulling that string. How far will you have to pull it to meet the conditions of this problem?
So is d then (5.5+0.85)m ?

Kenneth Dirk said:
So is d then (5.5+0.85)m ?
Where did the 0.85 m come from? (The radius?)

See if you can figure out how much string unwinds from the disk.

I suspect that the OP is making the problem more difficult than it has to be (I think you can get 4.3 m/s using a two-step method). Remember that the problem tells you what the net force on the disk is.

Last edited:
person123 said:
I suspect that the OP is making the problem more difficult than it has to be (I think you can get 4.3 m/s using a two-step method). Remember that the problem tells you what the net force on the disk is.
Quite so, but it is also important that the student come to understand why the attempted method went wrong.

person123

## 1. What is the formula for finding the speed of a rotating disk?

The formula for finding the speed of a rotating disk is v = rω, where v is the linear speed, r is the radius of the disk, and ω is the angular velocity.

## 2. How do you measure the radius of a rotating disk?

The radius of a rotating disk can be measured by using a ruler or measuring tape to measure the distance from the center of the disk to its outer edge.

## 3. Can the speed of a rotating disk be negative?

No, the speed of a rotating disk cannot be negative. The direction of the speed may change, but the numerical value will always be positive.

## 4. What are the units for the speed of a rotating disk?

The units for the speed of a rotating disk depend on the units used for the radius and angular velocity. Common units include meters per second (m/s), kilometers per hour (km/h), and revolutions per minute (rpm).

## 5. How does friction affect the speed of a rotating disk?

Friction can affect the speed of a rotating disk by slowing it down. The friction between the disk and its supporting surface can cause a decrease in the angular velocity, and therefore, a decrease in the linear speed of the disk.

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