Finding Velocity and Angular Speed of a Rolling Cylinder

In summary, the problem involves a solid cylinder with a radius of 20 cm rolling down a 2.5 meter incline without losing energy to friction. The velocity and angular speed of the cylinder at the bottom of the incline can be found by using the equations I = mr^2 and E = mgh, and taking into account the rotational and translational kinetic energy. The mass of the cylinder is not necessary for solving the problem.
  • #1
gamer1319
12
0

Homework Statement



A solid cylinder of radius 20cm is released from a 2.5 high incline. If it rolls down without losing any energy to friction, find the cylinder's velocity at the bottom of the incline and the angular speed at the bottom of the incline.

Homework Equations





The Attempt at a Solution



I need to be given a mass to solve this! If I had a mass, I'd plug it into I = mr^2, find the inertia. With that, I'd plug it into E = mgh, and after i'd find W (angular velocity). Help!
 
Physics news on Phys.org
  • #2


Are you sure the masses don't cancel out? :)
 
  • #3


gamer1319 said:

Homework Statement



A solid cylinder of radius 20cm is released from a 2.5 high incline. If it rolls down without losing any energy to friction, find the cylinder's velocity at the bottom of the incline and the angular speed at the bottom of the incline.

Homework Equations





The Attempt at a Solution



I need to be given a mass to solve this! If I had a mass, I'd plug it into I = mr^2, find the inertia. With that, I'd plug it into E = mgh, and after i'd find W (angular velocity). Help!

The mass is m. You don't need to know the mass with this problem any more than you need to know the mass of an object to find its final speed after falling 2.5 meters, if it was released at rest.

Don't forget, the final Kinetic Energy, KE, includes a rotational part as well as a translational part, i.e. KE = (1/2)·I·ω2 + (1/2)·m·v2 .
 

1. How does the shape of a solid cylinder affect its rolling motion?

The shape of a solid cylinder plays a crucial role in its rolling motion. Due to its circular shape, a solid cylinder has a higher moment of inertia compared to other shapes, making it more resistant to changes in motion. This results in a more stable and predictable rolling motion.

2. What factors influence the speed of a solid cylinder as it rolls down an incline?

The speed of a solid cylinder rolling down an incline is affected by several factors, including the mass of the cylinder, the angle of the incline, and the presence of any external forces, such as friction. The higher the mass and steeper the incline, the faster the cylinder will roll.

3. How does the surface material affect the rolling friction of a solid cylinder?

The surface material of a solid cylinder can greatly affect its rolling friction. A rougher surface will create more friction, causing the cylinder to roll slower, while a smoother surface will result in less friction and a faster rolling motion.

4. What is the relationship between the radius of a solid cylinder and its rolling motion?

The radius of a solid cylinder is directly related to its rolling motion. A larger radius means a larger moment of inertia, resulting in a slower rolling motion and a smaller radius means a smaller moment of inertia, resulting in a faster rolling motion.

5. Can a solid cylinder roll without slipping?

Yes, a solid cylinder can roll without slipping. This occurs when the distance traveled by the center of the cylinder is equal to the distance traveled by the point of contact between the cylinder and the surface. This type of motion is known as pure rolling and is commonly seen in situations where there is minimal friction present.

Similar threads

Kinetic Energy of a Cylinder Rolling Without Slipping
    • Introductory Physics Homework Help
Replies
21
Views
1K
A cylinder of snow rolls down a hill gathering more snow -- calculate its speed
    • Introductory Physics Homework Help
2
Replies
39
Views
2K
Speed of cylinder rolling along a horizontal surface gathering snow (Solved)
    • Introductory Physics Homework Help
Replies
13
Views
889
Wooden sphere rolling on a double metal track
    • Introductory Physics Homework Help
3
Replies
97
Views
3K
Rolling cylinder or slipping cylinder reaches bottom first?
    • Introductory Physics Homework Help
Replies
5
Views
3K
Cylinder Rolling Down an Incline Without Slipping
    • Introductory Physics Homework Help
Replies
7
Views
2K
Velocity of a hollow cylinder at the bottom of an incline
    • Introductory Physics Homework Help
Replies
9
Views
3K
Cylinder rolling down the hill
    • Introductory Physics Homework Help
Replies
5
Views
1K
Rotation of a Solid Cylinder
    • Introductory Physics Homework Help
Replies
12
Views
2K
What is the final angular velocity of each cylinder
    • Introductory Physics Homework Help
Replies
1
Views
1K

Hot Threads

Recent Insights

Back
Top