Center of Mass

Centre of mass

The center of mass is the point where we can assume all the mass of the object is concentrated.As the gravity only acts at a single point in the object. So a single arrow on diagram can represent the weight of the object.The centre of mass for regularly shaped objects is in the center.For irregular shaped objects,we can find the center of mass by following steps.

  1. Hang up the object.
  2. Suspend a plumb line from the same place.
  3. Mark the position of the thread.
  4. The centre of mass is along the line of thread.
  5. Repeat the above steps with object suspended from different places.
  6. The centre of mass is where these lines cross.

Centre of mass links stability:

It is important to know where the centre of mass of a body is, as its position determines the stability of the body.

A body is stable if, when it is tilted slightly, the line of action of its weight passes through its base.

EXPERIMENT TO DETERMINE CENTRE OF GRAVITY  OF PLANE LAMINA

Apparatus:

  • retort stand
  • cork
  • plumb line
  • pin
  • lamina

Experiment to determine centre of gravity of plane lamina

Experiment to determine centre of gravity of plane lamina

Procedure:

  1. On the lamina, make three holes near the edge of the lamina.
  2. Suspend the lamina through one of the holes as shown in the diagram.
  3. Hang the plumb line on the pin.
  4. When the plumb line is steady, make a dot on the position of the line at the edge of the lamina
  5. Repeat steps 2-4 for the other two holes

the point where the lines meet is the centre of mass of the body

Center of mass little story

My parents brought me back this wine holder from their most recent holiday.

wine-holder-empty

It doesn’t look much like a wine holder until you insert a bottle; whereupon it magic­ally “stands up”.

wine-holder-full-bottle-horizontal

An object bal­ances when its centre of mass is above its base. The base of the holder can be any point along the curved edge; the curved shape allows it to pivot freely. The holder bal­ances when the centre of mass is dir­ectly above the pivot.

wine-holder-full-bottle-horizontal-overlay

If the centre of mass is to the left of the pivot the holder rotates to move the the centre of mass right (anti­clock­wise); if it’s to the right then the holder moves the centre of mass to the left (clockwise).

An object free to rotate will rotate around its centre of mass. In the pho­to­graph below (click to enlarge) you can see where the centre of mass is — it hasn’t rotated and there­fore isn’t blurred.

wine-holder-oscillating

An empty bottle works just as well. A bottle uni­formly full of air and a bottle uni­formly full of water have almost the same centres of mass.

wine-holder-empty-bottle-horizontal

Shifting the neck of the bottle in and out of the holder shows what effect moving the centre of mass has on the balance point. With the neck all the way in the centre of mass is moved to the right and the holder bal­ances further to the right; the opposite is true when the neck is all the way out, moving the centre of mass to the left.

wine-holders-empty-positions

A half-full bottle has a very dif­ferent centre of mass; the ability of the water to move around causes the centre of mass to move around. In the pho­to­graph below the water has settled to the bottom of the bottle, moving the centre of mass towards the left as in the pho­to­graph above right.

wine-holder-half-full-bottle

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