Calculating Sphere Velocity on a Frictionless Ramp

In summary, the sphere is trying to calculate its linear and angular velocities, but is confused because of the difference between the two.
  • #1
kotchenski
16
0

Homework Statement


As of the past few hours I've been trying to make sense one how to calculate the velocity of a sphere that moves down a frictionless ramp. My biggest problem with this seems to be that I'm confusing myself with the linear velocity and the angular velocity. Note that the sphere starts at rest.


Homework Equations


Conservation of energy:
[tex]mgh=\frac{1}{2}mv^2 + \frac{1}{2}I \omega ^2 [/tex]

Relation between linear velocity and angular velocity
[tex] v= \omega r [/tex]


The Attempt at a Solution


I can get as far as equating the two and inserting the moment of inertia for a sphere.
[tex] mgh=\frac{1}{2}mv^2 + \frac{1}{2}(\frac{2}{5}mr^2 \omega ^2) [/tex]
Unfortunately now I have no clue how to proceed. I'm in a sort of dilemma where I know if it starts sliding down the ramp then it doesn't seem like there should be any rotation. But if there is no rotation then is there any point in including the final part of the equation? Of course I could always refer this to the kinetic friction and come up with some sort of argument but I just don't seem to understand how it can make it make sense.
 
Physics news on Phys.org
  • #2
Is the ramp frictionless or not? As you suspect, if there's no friction the sphere will not begin to rotate but will merely slide down.

What's the exact statement of the problem?
 
  • #3
The ramp is frictionless.

I'm trying to understand what is happening with the sphere. If it is not rolling is it necessary to include the angular velocity? I'm asking because it it's not rolling then wouldn't it be zero?

I have to do this so I can isolate the velocity to see how it changes for the sphere when the height increases or decreases.
 
  • #4
kotchenski said:
The ramp is frictionless.

I'm trying to understand what is happening with the sphere. If it is not rolling is it necessary to include the angular velocity? I'm asking because it it's not rolling then wouldn't it be zero?
Yes. Without friction ω = 0, so you can drop the rotational KE term from your energy equation.
 
  • #5
Doc Al said:
Yes. Without friction ω = 0, so you can drop the rotational KE term from your energy equation.

Thank you, that was just what I was looking for.
 

FAQ: Calculating Sphere Velocity on a Frictionless Ramp

What is a sphere on a frictionless ramp?

A sphere on a frictionless ramp is a classic physics problem that involves a spherical object rolling down a ramp with no friction or other external forces acting on it. This allows for simplified calculations and a better understanding of the principles of motion and energy.

How does a frictionless ramp affect the motion of a sphere?

A frictionless ramp eliminates the force of friction, which would normally act against the rolling motion of the sphere. This means that the sphere will continue to roll without slowing down or stopping, as there is no resistance to its motion.

What factors affect the motion of a sphere on a frictionless ramp?

The motion of a sphere on a frictionless ramp is affected by the angle of the ramp, the mass and size of the sphere, and the height of the ramp. These factors determine the potential and kinetic energy of the sphere, which in turn affect its speed and acceleration.

How does the height of the ramp affect the speed of the sphere?

The height of the ramp determines the potential energy of the sphere. The higher the ramp, the more potential energy the sphere has, which will be converted into kinetic energy as it rolls down the ramp. This means that a higher ramp will result in a faster speed for the sphere.

Can a sphere on a frictionless ramp ever stop rolling?

No, a sphere on a frictionless ramp will continue to roll without stopping unless acted upon by an external force. This is because there is no force of friction to slow it down, and the sphere will continue to convert potential energy into kinetic energy as it moves down the ramp.

Similar threads

Calculate the magnetic moment of a rotating sphere
Replies
17
Views
1K
How high does the frictionless ramp have to be for the ball....
Replies
5
Views
1K
Conservation of energy problem: Ball rolling down inclined plane and then through a loop-the-loop
Replies
10
Views
1K
How Does Angular Momentum Conservation Affect Asteroid Collision Dynamics?
10
Replies
335
Views
11K
Wooden sphere rolling on a double metal track
3
Replies
97
Views
4K
How Does a Frictionless Ramp Affect Loot Crate Motion?
Replies
6
Views
2K
Inelastic collision: block moving down a frictionless ramp
Replies
4
Views
4K
Is this formula for a ball rolling down a ramp incorrect?
Replies
10
Views
2K
Brownian Ratchet (exercise framed by Feynman's Lectures, l. 46)
Replies
32
Views
2K
2D kinematics problem -- Skateboard ramp jump calculations
Replies
4
Views
2K

Hot Threads

Recent Insights

Back
Top