# How Do You Calculate the Linear Speed of a Rolling Disc?

• public_enemy720
In summary, a problem involving a disc rolling along a flat plane with a constant force of 12N applied to the axle was discussed. The mass, diameter, and rotational inertia of the disc were given, and the question was to find the linear speed of the center of the disc after rolling for 12m. The conversation included a discussion of equations and a hint was given to use the relationship between tangential acceleration and angular acceleration. Finally, the solution involved using the total kinetic energy and work done on the wheel to solve for the linear speed.
public_enemy720
One more problem on a tough worksheet...I have tried it for a while, but can't find an equation(s) suitable for the problem...

A constant force of 12N is applied to the axle of a disc rolling along a flat plane. The disc has mass m=22kg, diameter D=.50m, and rotational inertia I=.688kgm^2. What is the linear speed of the center of the disc, V, after it has rolled for 12m?

I drew a free body diagram, and I know that the sum of the moments is equal to I times alpha, and I know the good ol' F=ma. But I can't seem to be able to find an acceleration with what I am given. A hint would be wonderful.

Oh boy...I went somewhere, but I don't know if it was right. Here is what I did:

I used m*a=f-f(friction) and friction*radius = I*alpha. Alpha is equal to a*r, so I plugged that into make friction times radius = I*a*radius.

Plugging that into m*a=F-f(friction) i got:

This is rather confusing, but I think it is somewhat correct. Any suggestions or gross errors on my part?

public_enemy720 said:
Oh boy...I went somewhere, but I don't know if it was right. Here is what I did:

I used m*a=f-f(friction) and friction*radius = I*alpha. Alpha is equal to a*r, so I plugged that into make friction times radius = I*a*radius.

Plugging that into m*a=F-f(friction) i got:

This is rather confusing, but I think it is somewhat correct. Any suggestions or gross errors on my part?
Right idea, but alpha does not equal a*r. alpha and a are certainly related and you need that relationship, but that is not it.

vijay123 said:

$$a_{T}=\alpha \cdot r$$, i.e. tangential acceleration equals angular acceleration times radius.

total K = (1/2)*m*v^2 + (1/2)*I*w^2

actually you don't have to use I = 0.688 which is given if you know the I of the disk is (1/2)*m*r^2.

plug all in, find out K = 3/4 * m * v^2

next,

the work does on the wheel also equals to the total K above. W = F*s = 12*12 = 144J

solve for v.

Good luck.

Minh T. Le

## 1. What is rotational motion of a disc?

Rotational motion of a disc refers to the movement of a disc around its central axis. This type of motion can be described by the disc's angular velocity, which is the rate at which it rotates, and its moment of inertia, which is its resistance to changes in rotational motion.

## 2. What causes rotational motion of a disc?

Rotational motion of a disc is caused by a force applied at a distance from the disc's central axis, known as a torque. The torque causes the disc to rotate and can be created by a number of factors such as friction, gravity, or an external force.

## 3. How is rotational motion of a disc different from linear motion?

Rotational motion and linear motion are two types of motion that differ in the path of movement. In rotational motion, the object moves around a fixed axis, while in linear motion, the object moves along a straight line. Additionally, rotational motion involves angular velocity and moment of inertia, while linear motion involves velocity and mass.

## 4. How is rotational motion of a disc measured?

Rotational motion of a disc is measured using angular displacement, which is the angle through which the disc rotates, and angular velocity, which is the rate of change of the angular displacement. These measurements can be obtained using tools such as a protractor, tachometer, or gyroscopic sensor.

## 5. What are some real-world applications of rotational motion of a disc?

Rotational motion of a disc has various applications in everyday life, such as in vehicles with rotating wheels, in machinery with rotating parts, and in sports equipment like frisbees and yo-yos. It also plays a crucial role in the functioning of engines, turbines, and other rotating equipment in industries such as aviation, automotive, and power generation.

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