The Relationship Between Linear Velocity and Angular Velocity in Gear Rolling

What is the angular velocity of the double gear rolling on a stationary lower rack with a center velocity of 1.2 m/s?

To determine the angular velocity of the double gear rolling on a stationary lower rack with a center velocity of 1.2 m/s, we can use the relationship between linear velocity and angular velocity in gear rolling. When a gear rolls, it rotates around its center and also translates along its axis.

The concept of Gear Rolling

Gear rolling is a combination of rotational and linear motion that occurs when a gear moves along a surface. In this case, the double gear is rolling on a stationary lower rack, with its center moving at a velocity of 1.2 m/s.

Calculation of Angular Velocity

To calculate the angular velocity of the gear, we can use the formula:

ω = v/r

Where:

ω = Angular velocity

v = Linear velocity (given as 1.2 m/s)

r = Radius of the double gear (not given in the data)

Substituting the given values into the formula, we get:

ω = 1.2/r

Proportional Relationship

Although we cannot determine the exact value of the angular velocity without knowing the radius of the double gear, we can conclude that the angular velocity is directly proportional to the linear velocity of the center of the gear. This means that as the linear velocity of the center of the double gear increases, the angular velocity of the gear will also increase.