{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Center of Mass - Center of Mass The Center of Mass:Chap...

Info icon This preview shows pages 1–11. Sign up to view the full content.

View Full Document Right Arrow Icon
Center of Mass
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
The Center of Mass:Chap 13.2 n There is a special point in a system or object, called the center of mass , that moves as if all of the mass of the system is concentrated at that point. n The system will move as if an external force were applied to a single particle of mass M located at the center of mass n M is the total mass of the system
Image of page 2
Center of Mass, Coordinates n Consider the system is made up of many pieces labeled with the subscript i n The coordinates of the center of mass are n where M is the total mass of the system M = m i i
Image of page 3

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Center of Mass, position n The center of mass can be located by its position vector, r CM n r i is the position of the i th particle, defined by
Image of page 4
C of M, Example x cm = (1.0 m )1.0 kg + (2.0 m )1.0 kg + (0 m )2.0 kg 4.0 kg x cm = 0.75 m y cm = (0 m )1.0 kg + (0 m )1.0 kg + (2.0 m )2.0 kg 4.0 kg y cm = 1.0 m r r cx = x cn ˆ i + y cm ˆ j = 0.75 m ˆ i + 1.0 m ˆ j M 1 = M 2 = 1.0kg, M 3 = 2.0kg x cm = m i x i i M
Image of page 5

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Center of Mass, Example 2 n Both masses are on the x -axis n The center of mass is on the x -axis n The center of mass is closer to the particle with the larger mass
Image of page 6
C of M Example 2 r r cm = m 1 x 1 + m 2 x 2 m 1 + m 2 ˆ i e . g . take m 1 = 10. kg , x 1 = 1.0 m & x 2 = 10. m , m 2 = 1.0 kg r r cm = 10. + 10. 11 ˆ i = 1.8 m ˆ i
Image of page 7

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Center of Mass, Extended Object n Think of the extended object as a system containing a large number of particles n The particle distribution is small, so the mass can be considered a continuous mass distribution
Image of page 8
Center of Mass, Example n An extended object can be considered a distribution of small mass elements, D m n The center of mass is located at position r CM
Image of page 9

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Center of Mass, Extended Object, Coordinates n The coordinates of the center of mass of the object are
Image of page 10
Image of page 11
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}