# What is the final angular velocity of each cylinder

• samm12345
In summary, the problem is about two identical cylinders A and B with a mass of 4 kg and radius of 150 mm. Cylinder A has an initial angular velocity of 50 rad/s and comes into contact with cylinder B which is initially at rest. The coefficient of kinetic friction at the contact point D is uk. After slipping for a period of time, both cylinders attain constant angular velocities in opposite directions. The problem asks for the final angular velocity of each cylinder and the coefficient of kinetic friction uk. Using the relevant equations, T1 + U = T2, the solution requires determining the final angular velocities of both cylinders and solving for the coefficient of kinetic friction uk.
samm12345
Homework Statement
The uniform 4-kg cylinder A, of radius r = 150 mm, has an angular velocity w = 50 rad/s when it is brought into contact with an identical cylinder B which is at rest. The coefficient of kinetic friction at the contact point D is uk. After a period of slipping, the cylinders attain constant angular velocities of equal magnitude and opposite direction at the same time. Knowing that cylinder A executes three revolutions before it attains a constant angular velocity and cylinder B executes one revolution before it attains a constant angular velocity, determine
(a) The final angular velocity of each cylinder,
(b) The coefficient of kinetic friction uk.
Relevant Equations
T1 + U =T2
Problem Statement: The uniform 4-kg cylinder A, of radius r = 150 mm, has an angular velocity w = 50 rad/s when it is brought into contact with an identical cylinder B which is at rest. The coefficient of kinetic friction at the contact point D is uk. After a period of slipping, the cylinders attain constant angular velocities of equal magnitude and opposite direction at the same time. Knowing that cylinder A executes three revolutions before it attains a constant angular velocity and cylinder B executes one revolution before it attains a constant angular velocity, determine
(a) The final angular velocity of each cylinder,
(b) The coefficient of kinetic friction uk.
Relevant Equations: T1 + U =T2

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samm12345

## 1. What is angular velocity and why is it important?

Angular velocity is a measure of the rate at which an object rotates around a fixed axis. It is important because it helps us understand the motion of rotating objects, such as wheels, gears, and planets.

## 2. How is angular velocity calculated?

Angular velocity is calculated by dividing the change in angle (in radians) by the change in time. It is typically measured in radians per second (rad/s).

## 3. What factors affect the final angular velocity of a cylinder?

The final angular velocity of a cylinder is affected by its initial angular velocity, the applied torque, the moment of inertia, and any external forces or friction acting on the cylinder.

## 4. Can the final angular velocity of a cylinder be negative?

Yes, the final angular velocity of a cylinder can be negative if the cylinder is rotating in the opposite direction to its initial rotation. This is known as negative angular velocity or clockwise rotation.

## 5. How can the final angular velocity of each cylinder be measured?

The final angular velocity can be measured using tools such as a tachometer, which measures the speed of rotation, or by using mathematical equations that take into account the cylinder's dimensions and rotational properties.

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