Rolling motion of a cylinder down an incline

In summary, the conversation discusses the validity of an equation for calculating the acceleration of a solid cylinder down an incline, with the person mentioning that their measured acceleration values are smaller than the theoretical values. They also mention the possible presence of rolling resistance and the discrepancy between their measured and theoretical values. The conversation also includes a question about the correct units and methods for measuring acceleration.
  • #1
mlostrac
83
0

Homework Statement


Assuming smooth rolling with no resistance, it can be shown that the acceleration of a solid cylinder down an incline is equal to:

a = 2/3 g sin(theta)

The goal of my lab is to test the validity of the above equation


Homework Equations





The Attempt at a Solution


The acceleration values I found using my measured inclination angles, are smaller than what they would be if i plugged them into the above equation. What does this mean? If this is the case, does that mean that the above equation isn't valid?
 
Physics news on Phys.org
  • #2
Did you put your angle in radiants?
 
  • #3
mlostrac said:
Assuming smooth rolling with no resistance...

Were you able to eliminate all rolling resistance in your lab? With rolling resistance present would you expect acceleration to be higher or lower than theoretical? How close to theoretical were your measured accelerations?
 
  • #4
tvavanasd said:
Were you able to eliminate all rolling resistance in your lab? With rolling resistance present would you expect acceleration to be higher or lower than theoretical? How close to theoretical were your measured accelerations?

I'm not sure, but I'm going to assume that I didn't eliminate all resistance; I rolled a hockey puck on it's side down a wooden board.

I'd assume that if resistance was present that it would cause the acceleration to be lower than theoretical.

One example comparing theoretical and measure for a 5.7 degree incline:
theoretical = 0.649 m/s^2
measured = 0.073 m/s^2
 
  • #5
srmeier said:
Did you put your angle in radiants?

yes i did, 25.6 degrees = .46 rad
 
  • #6
mlostrac said:
I'd assume that if resistance was present that it would cause the acceleration to be lower than theoretical.

One example comparing theoretical and measure for a 5.7 degree incline:
theoretical = 0.649 m/s^2
measured = 0.073 m/s^2

Your assumption is correct, but the discrepency seems quite large.
How did you arrive at your measured accel?
Were you able to sample multiple points during the test or simply average over time and displacement?
How long was the ramp?
Did you find the theoretical vs measured to be closer as the ramp slope increased?

Shouldn't be significant, but 25.6 degrees is 0.447 radians.
 

1. What is rolling motion?

Rolling motion is a type of motion where a body, such as a cylinder, rotates and translates at the same time. In this case, the body is moving down an incline and also rotating around its own axis.

2. How does the incline affect the rolling motion of a cylinder?

The incline affects the rolling motion of a cylinder by providing a gravitational force that pulls the cylinder down the slope. This force, along with the normal force from the incline, causes the cylinder to accelerate and roll down the incline.

3. What factors affect the speed of the rolling cylinder?

The speed of the rolling cylinder is affected by several factors, including the angle of the incline, the mass of the cylinder, and the presence of any external forces, such as friction or air resistance. The shape and size of the cylinder can also play a role in its speed.

4. What is the difference between rolling motion and sliding motion?

The main difference between rolling motion and sliding motion is the presence of rotation. In rolling motion, the body rotates while moving, while in sliding motion, the body only translates without any rotation. This is why a cylinder rolling down an incline has a different motion compared to a block sliding down the same incline.

5. How is the energy of a rolling cylinder conserved?

The energy of a rolling cylinder is conserved because the cylinder experiences both translational and rotational motion. As the cylinder moves down the incline, its kinetic energy changes between translational kinetic energy and rotational kinetic energy. However, the total energy of the system remains constant, as long as there are no external forces acting on the cylinder.

Similar threads

  • Introductory Physics Homework Help
Replies
21
Views
1K
Replies
24
Views
1K
  • Introductory Physics Homework Help
2
Replies
35
Views
2K
  • Introductory Physics Homework Help
Replies
9
Views
456
Replies
39
Views
1K
  • Introductory Physics Homework Help
Replies
11
Views
1K
  • Introductory Physics Homework Help
Replies
7
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
788
Replies
2
Views
1K
  • Introductory Physics Homework Help
Replies
18
Views
3K
Back
Top