Rolling cylinder on an incline

[andrewp7]

A cylinder of a mass M and a radius R starts at the top of a hill at a height h, and rolls to the bottom. At the bottom of the hill, what is its linear velocity, linear momentum, and angular momentum?


I believe the the velocity is sqrt((4/3)gh) and the the angular momentum is mvsin(theta) but I am not sure if those are right and I still d not know the linear momentum

 

[ehild]

You have to give all quantities in terms of M, R, and h. Theta is not given. Look after the definition of angular momentum, it is not mvsin(theta). The linear momentum is the same as the momentum of the CM of the cylinder.

ehild

 

[andrewp7]

wouldn't I need some type of angle because it is on an incline?

 

[ehild]

Do you? You got the speed without the angle, don't you? How did you got it? Using what law?

ehild

 

[rwisz]

.I can provide a response to the content regarding the rolling cylinder on an incline. First, let's define some of the variables mentioned in the scenario:

- Mass (M): This refers to the amount of matter contained within the cylinder, measured in kilograms (kg).
- Radius (R): This is the distance from the center of the cylinder to its outer edge, measured in meters (m).
- Height (h): This is the vertical distance from the top of the hill to the bottom, measured in meters (m).
- Linear velocity: This is the speed of the cylinder in a straight line, measured in meters per second (m/s).
- Linear momentum: This is the product of mass and velocity, and it represents the quantity of motion in a straight line, measured in kilogram meters per second (kg m/s).
- Angular momentum: This is the product of moment of inertia and angular velocity, and it represents the quantity of rotational motion, measured in kilogram meters squared per second (kg m^2/s).

Now, let's look at the scenario. The cylinder starts at the top of the hill with an initial potential energy due to its height. As it rolls down the incline, this potential energy is converted into kinetic energy, resulting in an increase in linear velocity. At the bottom of the hill, all of the potential energy has been converted to kinetic energy, and the cylinder has reached its maximum velocity.

To calculate the linear velocity at the bottom of the hill, we can use the conservation of energy principle, which states that the total energy of a system remains constant. In this case, the initial potential energy (mgh) is equal to the final kinetic energy (1/2mv^2). Therefore, we can use the equation mgh = 1/2mv^2 to solve for the linear velocity (v), which gives us v = sqrt((2gh)). However, this only gives us the velocity at the bottom of the hill, and it does not take into account the radius of the cylinder.

To calculate the linear momentum, we can use the equation p = mv, where p represents linear momentum, m is the mass of the cylinder, and v is the linear velocity. Therefore, the linear momentum at the bottom of the hill would be p = m*sqrt((2gh)). This means that the linear momentum is directly proportional to the mass and the square root of the height and is independent of