# Angular Velocity Of A Wheel

• mrshappy0
In summary, the projectile strikes the wheel, sticking to it, and causes it to rotate. The angular speed of the wheel is found to be
mrshappy0

## Homework Statement

A wad of sticky clay with mass 2.45 kg and velocity vi = 52.0 m/s is fired at a wheel of moment of inertia 1.2 kg m2 and radius R = 1.26 m. The wheel is initially at rest and is mounted on a fixed horizontal axle that runs through its center of mass. The line of motion of the projectile is perpendicular to the axle and at distance d = 0.842 m from the center.
Find the angular speed of the cylinder (in rad/s) just after the clay strikes and sticks to the surface of the wheel.

T=rF=Iα.

## The Attempt at a Solution

I don't have a textbook with me so I am trying to work through this by searching the internet and my memory. I am thinking in order to solve this you would just take the angular force times the radius and you would have torque. Then from there you would find the angular speed from the torque but I don't see how you would find the torque if the problem only gives you the velocity of the clay projectile.

Since you don't have information of the forces involved, see if you can apply a conservation law to solve the problem.

Right as I finished typing I thought of conservation of momentum but isn't the clay piece an external force?

Meaning the momentum is not conserved from the initial state of the wheel to the final state.

mrshappy0 said:
Right as I finished typing I thought of conservation of momentum but isn't the clay piece an external force?
While the momentum of either one--clay piece or wheel--isn't conserved by itself, the momentum of the system (the angular momentum) is.

Oh okay! So does would the initial momentum of the clay equal mvd?

mrshappy0 said:
So does would the initial momentum of the clay equal mvd?
No. You must use the distance between the line of motion of the clay and the axis of rotation.

Which is d in this problem. Thanks for you help.

mrshappy0 said:
Which is d in this problem.
Ah, yes it is.

## 1. What is Angular Velocity?

Angular velocity is the rate of change of angular displacement of an object with respect to time. In simpler terms, it is the measure of how fast an object is rotating around a fixed axis.

## 2. How is Angular Velocity calculated?

Angular velocity is calculated by dividing the change in angular displacement by the change in time. It is typically measured in radians per second (rad/s) or degrees per second (deg/s).

## 3. What factors affect the Angular Velocity of a wheel?

The Angular Velocity of a wheel can be affected by several factors including the radius of the wheel, the speed of rotation, and the torque applied to the wheel.

## 4. How does Angular Velocity differ from Linear Velocity?

Angular Velocity measures the rate of change of angular displacement, while linear velocity measures the rate of change of linear displacement. Angular Velocity is measured in rotational units, while linear velocity is measured in linear units.

## 5. Why is Angular Velocity important?

Angular Velocity is important because it helps us understand the motion of rotating objects and how they interact with other objects. It is also used in various fields such as engineering, physics, and astronomy to analyze the behavior of rotating systems.

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