5 - centres of mass 1

Question 1

centre of mass of two identical particles

Answer 1

midpoint of the straight line between them

Question 2

if the masses of particles are different you find the CoM by

Answer 2

caclulating a weighted average
x = m1x1+m2x2… /m1+m2

Question 3

fromula to find centre of mass of particles

Answer 3

Mx = m1x1+m2x2…+ mnxn
where M = m1+m2…+mn

Question 4

CoM of particles arranged in a plane

Answer 4

M(x,y) = m1(x1,y1) + m2(x2,y2)… mn(xn, yn)

Question 5

CoM of a uniform rod

Answer 5

midpoint

Question 6

CoM of a uniform lamina

Answer 6

lies on any axis of symmetry
if there are multiple then it lies at the intersection of these

Question 7

lamina

Answer 7

2D object
assume the lamina has zero thickness
uniform = constant mass per unit area

Question 8

CoM of a uniform triangular lamina

Answer 8

add up coordinates of the corners and average
x = x1+x2+x3 /3
y = y1+y2+y3 /3

Question 9

CoM of the sector of a circle

Answer 9

2rsin⍺/3⍺
where 2⍺ is the angle of the sector in radians

Question 10

CoM of a uniform wire bent to form an arc

Answer 10

rsin⍺/⍺
where 2⍺ is the angle of the sector in radians

Question 11

CoM of composite bodies

Answer 11

table of shape, length/ vol/ area and CoM
then use the formula