a. How far from the corner is the center of mass for this object. Express answer

Question

a. How far from the corner is the center of mass for this object. Express answer in terms of L

b. The corner shaped is balaced on a pivot as shown and then displaced from vertical by an angle theta. write an appropriate equation of motion of the corner-shaped object. Express answer in terms of L and theta. Show steps.

c.For this arrangement ,find the time for the corner shape to make one complete oscillation. Assume small amplitude oscillations. Express answer in terms of L. Show all steps please.

Explanation / Answer

1) CM= (L/2)cos45=0.35L from the corner

2) Considering the Center of mass(CM),

mg(L/22)(1-cos)=mv2/2

v=(g/2)(1-cos)

3) T=4(2h/g) = 4(L/2)(1-cos)g= 4(L/g2)(2sin2(/2))= 4sin(/2)(L2/g)

f= 1/4sin(/2)(L2/g)

for small amplitude oscillations, sin(/2)=/2

f=(1/2)((g/L2)

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