The discussion centers on the concept of center of mass as it pertains to a hammer and ruler balance system. The center of mass of the hammer is located near the hammer head, which influences the stability of the mobile system. For stability, the center of mass must be positioned directly below the pivot point, which is the edge of the table or the part of the ruler resting on it. If the center of mass is displaced from this position, the system will not immediately collapse but will tend to return to equilibrium due to the restoring force generated by the weight of the hammer.
PREREQUISITESStudents of physics, educators explaining mechanics, engineers designing stable structures, and anyone interested in the principles of balance and stability in physical systems.
Where's the center of mass of the hammer?tanyh123 said:How do I explain this in terms of centre of mass?
The same as it is in any context. Think of it as the (weighted) average location of the mass.And what's the definition of centre of mass in this context?
Doc Al said:Where's the center of mass of the hammer?
Doc Al said:The same as it is in any context. Think of it as the (weighted) average location of the mass.
CWatters said:The center of mass is below the pivot point therefore the system is inherently stable.
Right.tanyh123 said:The centre of mass of the hammer is near the hammer head, so the centre of mass of the whole mobile should be found there as well?
The center of mass must be under the part of the ruler resting on the table.Does the centre of mass of the mobile have to be vertically aligned with the table and a part of the ruler which is resting on the table or does it have to be under the table only?
Explain what? The center of mass does not have to be located where there is any mass. Think of it as a mathematical point that is useful for describing the behavior of a system, not as a part of a body.But the centre of gravity of a donut is found around the centre of the donut, which is actually empty space. How do I explain that then?
CWatters said:The center of mass is EXACTLY below the pivot point (eg like a stationary pendulum).
The question is where is the pivot point? In the example photo it can move. It can be anywhere between the edge of the table or the right hand end of the ruler. This actually helps increase stability...
If the hammer is disturbed by pushing/swinging it slightly to the left the pivot point will probably move to the right hand end of the ruler. This increases the restoring force on the hammer.
If the hammer is disturbed by pushing it slightly to the right the pivot point will probably move to the left eg the edge of the table. This also increases the restoring force on the hammer.
If you displace the hammer from its equilibrium position, its weight will create a torque that tends to bring it back to equilibrium. Imagine you had a ball on the end of a string, hanging down from your hand. If you move the ball aside, it will naturally tend to swing back. Same idea.tanyh123 said:What do you mean by restoring force?
No. When released from that point, it will tend to return to its equilibrium position.And if the hammer is disturbed to an extent where the centre of mass is no longer under the pivot point, the mobile will collapse, won't it?
tanyh123 said:What is required for it to fall?