Imagine we have a right hand co ordinate system( i.e X cross Y is Z).Take a half sphere and place it on the XY plane such that its flat part touches the YZ plane and its bulging part points towards positive X axis.The point on the XY plane where the half sphere touches it is the origin.Now the com of this half sphere is given a velocity V towards positive Y Axis.What will be the co ordinates of the COM when the half sphere comes to rest.The friction coefficient between the sphere and the X Y plane is k.Gravity is in the direction of negative Z axis.The mass of the half sphere is M and its radius is R.
The "corn"? Why not the peas or rice? Maybe this means something in British English that is different from American English.
QUOTE (Subduction Zone+Apr 3 2011, 03:59 PM)
The "corn"? Why not the peas or rice? Maybe this means something in British English that is different from American English.
hahahaha..brother it is COM ..centre of mass..
hahahaha..brother it is COM ..centre of mass..
QUOTE (Umer.banday+Apr 3 2011, 04:32 PM)
hahahaha..brother it is COM ..centre of mass..
Oops, my bad. On my screen when I see COM in lower case it looks like corn. I am not the only one who has problems with the way that letters show up here.
That makes a lot more sense by the way, thank you.
Oops, my bad. On my screen when I see COM in lower case it looks like corn. I am not the only one who has problems with the way that letters show up here.
That makes a lot more sense by the way, thank you.
QUOTE (Umer.banday+Apr 3 2011, 06:17 AM)
What will be the co ordinates of the COM when the half sphere comes to rest?
Why would it come to rest?
Why would it come to rest?
QUOTE (Smulan+May 10 2011, 08:38 PM)
Why would it come to rest?
Friction.
Friction.
QUOTE (boit+May 15 2011, 05:00 AM)
Friction.
Friction between which surfaces?
Friction between which surfaces?
QUOTE (Smulan+May 15 2011, 09:01 PM)
Friction between which surfaces?
Oops! I thought the YZ plane was physical and the coefficient of friction k was between it and the hemisphere's flat surface . It now appears to me that the only physical plane is XY and there is friction between the hemisphere and this plane. If this be the case, the sphere will topple to its bulging side and come to rest in short order due to gravity. Its motion will be a curve to the right (i.e. Positive X axis). Another scenerio will see it curve further to head back towards negative Y or even make a full circle. Without a push to the com it will of course topple to its bulging end immediately you stop propping it up. I hope I got that one right.
Oops! I thought the YZ plane was physical and the coefficient of friction k was between it and the hemisphere's flat surface . It now appears to me that the only physical plane is XY and there is friction between the hemisphere and this plane. If this be the case, the sphere will topple to its bulging side and come to rest in short order due to gravity. Its motion will be a curve to the right (i.e. Positive X axis). Another scenerio will see it curve further to head back towards negative Y or even make a full circle. Without a push to the com it will of course topple to its bulging end immediately you stop propping it up. I hope I got that one right.
QUOTE (boit+May 16 2011, 03:24 AM)
... there is friction between the hemisphere and this plane.
Usually, friction is a concept used to model resistance to motion between surfaces. The question is posed in a way which suggests ideal objects and circumstances (no rolling resistance etc), in which case there is, as far as I can gather, nothing to stop neither the stipulated Y velocity nor the pendulum motion from gravity.
Usually, friction is a concept used to model resistance to motion between surfaces. The question is posed in a way which suggests ideal objects and circumstances (no rolling resistance etc), in which case there is, as far as I can gather, nothing to stop neither the stipulated Y velocity nor the pendulum motion from gravity.
How closely does this resemble the bicycle wheel with a rope supporting one end of the axle and we rotate the wheel? The rope is parallel to the Z axis. O.K this setup isn't translating and I know the physics governing moment of inertia of a disc is different from that of a sphere but am seeing some similarities. They both precess.
PS. The friction may be purely static friction, no rolling resistance/friction if we idealize the setup as you pointed.
PS. 2. I am just having a flight of ideas (that's my nature unfortunately). I'll email the OP so that he can give us more meat to chew
PS. The friction may be purely static friction, no rolling resistance/friction if we idealize the setup as you pointed.
PS. 2. I am just having a flight of ideas (that's my nature unfortunately). I'll email the OP so that he can give us more meat to chew
QUOTE (Smulan+May 10 2011, 08:38 PM)
Why would it come to rest?
Why do rolling wheels coast to a stop? Am not sure but according to Sithdarth (and established physics by extension), the answer is in the moment of inertia and conservation of angular momentum (at least that is what I think was said in the original Plane On a Conveyor thread. Let me do some checks. Damn this mobile phone browser!
Why do rolling wheels coast to a stop? Am not sure but according to Sithdarth (and established physics by extension), the answer is in the moment of inertia and conservation of angular momentum (at least that is what I think was said in the original Plane On a Conveyor thread. Let me do some checks. Damn this mobile phone browser!
Rolling wheels coast to a stop because of losses caused by rolling resistance. These losses occur through deformation at the interface between tire and surface and if the wheel has an axle because of energy losses there. Rolling resistance allows for violations of conservation of angular momentum by introducing outside forces. The moment of inertia just scales the rate of angular momentum loss with respect to the rate of energy loss. In this case there is no place for an axle or deformation so energy can't be lost that way. There is also no force pushing the sphere against the one surface said to have friction so there is no energy lost that way. As long as the sphere doesn't topple it should roll forever on it's edge or slide since I believe there was no mention of friction on the x-z plane.
Thanks for the clarification. I searched the forum for that statemet but couldn't open the link though I saw part of the explanation. So will this hemisphere translate in a straight line or wobble or just make a circular motion? Any precession?
QUOTE (Sithdarth+May 16 2011, 07:27 PM)
Rolling resistance allows for violations of conservation of angular momentum by introducing outside forces. The moment of inertia just scales the rate of angular momentum loss with respect to the rate of energy loss.
I'm not sure what you mean by this, but taken at face value, those statements aren't quite valid I think.
I'm not sure what you mean by this, but taken at face value, those statements aren't quite valid I think.
QUOTE (Sithdarth+May 16 2011, 07:27 PM)
As long as the sphere doesn't topple it should roll forever on it's edge or slide since I believe there was no mention of friction on the x-z plane.
Rolling isn't mentioned; barring gyroscopic effects, the half sphere will topple, leading to a pendulum motion.
The interface between the spherical part of an ideal half sphere and an ideal plane is a mathematical point; friction applies to surfaces.
The half sphere will slide in the Y direction whilst rocking madly, until hit by a plane on a conveyor that never took off.
Rolling isn't mentioned; barring gyroscopic effects, the half sphere will topple, leading to a pendulum motion.
The interface between the spherical part of an ideal half sphere and an ideal plane is a mathematical point; friction applies to surfaces.
The half sphere will slide in the Y direction whilst rocking madly, until hit by a plane on a conveyor that never took off.
[QUOTE] . . . .until hit by a plane on conveyor that never took off.[QUOTE]
LOL
LOL
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