# How Does Torque Affect Angular Velocity in a Falling Block and Wheel System?

• ~angel~
In summary, the conversation discusses the calculation of the angular speed of a bicycle wheel after a block of mass m falls a distance h when attached to the wheel at two different radii: r_A and r_B. Using conservation of mechanical energy, the angular speed, omega_A, for the case where the string is attached to the outside of the wheel can be expressed in terms of m, g, h, r_A, and I. Similarly, for the case where the string is attached to a smaller inside axle with radius r_B, the angular speed, omega_B, can be expressed in terms of the same variables. It is not necessary to consider torque in this problem.
~angel~
Consider a bicycle wheel that initially is not rotating. A block of mass m is attached to the wheel and is allowed to fall a distance h. Assume that the wheel has a moment of inertia I about its rotation axis.

Consider the case that the string tied to the block is attached to the outside of the wheel, at a radius r_A. Find omega_A, the angular speed of the wheel after the block has fallen a distance h, for this case.
Express omega_A in terms of m, g, h, r_A, and I.

Now consider the case that the string tied to the block is wrapped around a smaller inside axle of the wheel of radius r_B View Figure . Find omega_B, the angular speed of the wheel after the block has fallen a distance h, for this case.
Express omega_B in terms of m, g, h, r_B, and I.

Someone told me that I have incorporate torque into it. I initially thought that you needed to use the conservation of energy, etc. Any help would be great.

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You are correct. It is not necessary to consider torque in this problem. You need to use conservation of mechanical energy. The gravitational potential energy of the elevated mass is released as it falls and converted into the linear and rotational kinetic energies of the mass and the wheel, respectively.

## 1. What is wheel and angular velocity?

Wheel and angular velocity refers to the rate at which a wheel rotates around its axis. It is measured in units of radians per second (rad/s) or revolutions per minute (rpm).

## 2. What is the relationship between wheel and angular velocity?

The relationship between wheel and angular velocity is that they are directly proportional. This means that as the wheel rotates faster, the angular velocity increases, and vice versa.

## 3. How is wheel and angular velocity calculated?

Wheel and angular velocity can be calculated by dividing the angular displacement (in radians) by the time it takes for the wheel to complete one full rotation. It can also be calculated by multiplying the linear velocity (in meters per second) by the radius of the wheel.

## 4. Why is wheel and angular velocity important?

Wheel and angular velocity are important in many scientific and engineering applications, such as in the design of vehicles, machines, and tools. It is also essential in understanding the principles of rotational motion and angular momentum.

## 5. How does wheel and angular velocity relate to centripetal and centrifugal forces?

Wheel and angular velocity are directly related to centripetal and centrifugal forces. As the wheel rotates, a centripetal force is required to keep it moving in a circular path, while a centrifugal force acts in the opposite direction. The magnitude of these forces is dependent on the angular velocity of the wheel.

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