Chapter 10, Problem 19A

Three types of rollers are placed on slightly inclined parallel meter stick tracks, as shown below. Rank the rollers, in terms of their ability to remain stable as they roll, from greatest to least.

To determine

To rank: The rollers in terms of their ability to remain stable from greatest to least.

Answer to Problem 19A

The rank of the rollers in terms of their ability to remain stable as they roll from greatest to least is $C>A>B$ .

Explanation of Solution

Given:

The given figure representing the rollers is shown below:

  

Formula used:

The expression for the linear or tangential speed is,

  $v=r\omega$

Here, $r$ is the radial distance and $\omega$ is the angular velocity.

Tangential speed is dependent on the distance from the axis of rotation and rotational speed.

Calculation:

The linear speed is directly proportional to the radius of its circular path.

For case A:

Both the ends of roller A have the same radius. So the ends of roller A are moving with the equal speed.

The roller will not stay on the inclined parallel meter stick track a long time.

The roller A moving along the track about the center.

For case B:

The radius of the two ends of roller B is greater than the radius of the middle of roller B. So the speed at the roller B is more when compared to the other rollers on the track.

Due to the wider radius of roller on track, it tends to turn the wheels off the track.

The roller B moving along the track and will not stay while rolling.

For case C:

The radius of the two ends of roller C is less than the radius of the middle of roller C. So the speed at the roller C is more and it travels a greater distance per revolution.

The roller will stay on the inclined parallel meter stick track and roll along the meter stick track. The pair of cups in which is towards the center.

By comparing the circular path is $C>A>B$ .

Conclusion:

Thus, the rank of the rollers in terms of their ability to remain stable as they roll from greatest to least is $C>A>B$ .