Center of Mass and Linear Momentum Formulas

Question 1

Center of mass

Answer 1

xcom = 1/M Σ mi xi

Question 2

Newtons second law for a system of particles

Answer 2

Fnet = M acom

Question 3

Linear Momentum (p) single particle

Answer 3

p = mv
Fnet = dp/dt

Question 4

Linear Momentum system of particles (P)

Answer 4

P = M v com
Fnet = dP/dt

Question 5

impulse - linear momentum theorem

Answer 5

change in linear momentum (pf - pi) = J

Question 6

impulse due to force

Answer 6

J = integral of F(t) dt
J = Favg (△t)

Question 7

Average force on a fixed body (collision and impulse)

Answer 7

Favg = -(n/△ time) (△ linear momentum p)
Favg = -(n/△t) (m△v)
Favg = -(△m/△t) (△v)

Question 8

Conservation of linear momentum (system of particles P)

Answer 8

Pi = Pf
P = constant

Question 9

Inelastic Collision in One dimension

Answer 9

p1i + p2i = p1f + p2f
m1 v1i + m2 v2i = m1 v1f + m2 v2f

Question 10

Elastic Collision in One Dimension

Answer 10

v1f = [(m1 -m2)/(m1+m2)] v1i
v2f = [2m1 / (m1 + m2)] v1i

Question 11

Collision in Two Dimensions (Inelastic)

Answer 11

P1i + P2i = P1f + P2f

Question 12

Collision in Two Dimensions (elastic)

Answer 12

K1i + K2i = K1f + K2f

Question 13

Variable Mass (first rocket equation)

Answer 13

Rvrel (thrust) = Ma

Question 14

Variable Mass (second rocket equation)

Answer 14

vrel is the exhaust speed
vf -vi = vrel ln (Mi/Mf)