Problem: Meter Stick Pendulum Consider pendulum formed from a meter stick pinned

Question

Problem: Meter Stick Pendulum

Consider pendulum formed from a meter stick pinned at the end. The center of mass (COM) is at the middle of the ruler, and the COM rotational inertial is (see Table 10.2 in text) for meter( Text is principles of physics by Serway & Jewett). When the meter stick is pinned at distance L from the COM, the rotational inertia becomes:

I = Io + ML^2 = Ml^2/12 +ML^2

We can compute the period T in seconds for a meter stick pinned at the end (L= L/2) when dropped from a small angle

l = lo = ML^2 = ML^2/12 + ML^2/4 = ML^2/3

T = 2pill square root I/(MgL) = 2pill square root 4/3 * square root L/g

Suppose the mass or the meter stick is M = 100 grams. Compute the moments of inertia I and the periods T for the pendula created by pivoting at the following distances L (measured from the COM)

L(m) I(kg-m^2) T(sec)

0.5

0.3

0.1

Explanation / Answer

For L = 0.5 m: I = 0.03333333 kg/m^2 T = 1.63878206 s, For L = 0.3 m: I = 0.01733333 kg/m^2 T = 1.52562307 s, For L = 0.1 m: I = 0.00933333 kg/m^2 T = 1.93903308 s

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