SPME 425

SPME 430

Homework #6 - Moment of Inertia & Angular Momentum

PART I

Using the same information provided in Homework #5, compute the following:

I _KNEE- Moment of inertia about an axis through K and parallel to Y.

K - knee joint

S - center of mass of the shank

F - center of mass of the foot

r_s = 0.10 i + 0j - 0.20 k m

r_f = 0.30 i + 0j - 0.50 k m

I _{CG SHANK} = 0.040 kg m²

I _{CG FOOT}= 0.003 kg m²

^m_SHANK^{= 3.0 kg}

^m_FOOT^{= 1.0 kg}

^w_{SHANK + FOOT}^{= -3.0 j rad/s}

^a_{SHANK + FOOT}^{= -500.0 j rad/s2}

PART II

Calculate the local term, transfer term and total angular momentum of the shank of the long jumper relative to the c.g. of the body.

Bold face type is used to indicate vectors.

a) Location of the c.g. of the shank relative to the c.g. of the body:

r_s = [ - 0.30 i - 0.50 j ] m

b) Velocity of the c.g. of the shank relative to the c.g. of the body:

v_s = [ 3.7 i + 1.0 j ] m/s

c) Angular velocity of the shank about its own c.g.

w_s = [ -5 k ] rad/s

d) Mass of the shank:

m_s = 3.5 kg

e) Moment of inertia of the shank relative to a transverse axis passing through its c.g.

I_s = 0.05 kgm²