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# Purpose - Lab 4 Rigid Pendulum Muhammad Usama Arabi 5267668...

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Lab 4 - Rigid Pendulum Muhammad Usama Arabi 5267668 Alison Harman Section 12-b August 1 st 2011 Department of Physics

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Purpose: The purpose of this lab was to determine an experimental value of gravitational acceleration. This value will be calculated using the observations of simple, rigid and torsional pendulums. The experimental value is expected to be within 1% of the literature value for acceleration due to gravity which in 9.81m/s 2 . Theory: To complete the calculations involved in this lab the following formulas were used: Rigid Pendulum Equation: This equation is typically used to calculate the theoretical period of oscillation T using the following terms: I - moment of inertia (kg/m 2 ) M - mass of the oscillating pendulum (kg) h - height of the pivot point from the center of mass (m) T - period of oscillation (s) Derived formula for g: Use equations (2) and (3): Rearrange for the torsional constant C: The modified equations (2) and (3) are equated by the torsional constant to obtain equation (4): Use the given moment of Inertia of the bar, equation (5), and sub it into equation (4):
Use the parallel axis theorem to determine the exact moment of inertia of the rigid pendulum: Now we must substitute this equation into the initial Rigid Pendulum equation and derive and expression for g : 3. Procedure For procedure please refer to lab 4 pages 1-3 in the Physics Laboratory Manuel for First year Science Students. 4. Results 4.1 Masses and dimensions Table 1: Masses and dimensions M (kg) 1.8383± 0.0001 M bar (kg) 1.8603± 0.0001 h (m) 0.509± 0.0005 L (m) 0.602± 0.0005 b (m) 1.9x10 -2 ± 0.0005 3.2, 3.3, 3.4, 3.5 Table 2.1: Time of Oscillation Trial t bar (for 25 oscillations)(s) T(for 50 oscillations)(s) T o (for 25 oscillations) (s) 1 160.75± 0.5 79.97± 0.5 246.69± 0.5 2 160.96± 0.5 79.44± 0.5 246.87± 0.5 3 160.51± 0.5 79.94± 0.5 246.73± 0.5

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Purpose - Lab 4 Rigid Pendulum Muhammad Usama Arabi 5267668...

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