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We measured \(g = 7.65\pm 0.378\text{m/s}^{2}\). Fair use is a use permitted by copyright statute that might otherwise be infringing. For the precision of the approximation sin \(\theta\) \(\theta\) to be better than the precision of the pendulum length and period, the maximum displacement angle should be kept below about 0.5. Recall from Fixed-Axis Rotation on rotation that the net torque is equal to the moment of inertia I = \(\int\)r2 dm times the angular acceleration \(\alpha\), where \(\alpha = \frac{d^{2} \theta}{dt^{2}}: \[I \alpha = \tau_{net} = L (-mg) \sin \theta \ldotp\]. If you would like to change your settings or withdraw consent at any time, the link to do so is in our privacy policy accessible from our home page.. Theory A simple pendulum may be described ideally as a point mass suspended by a massless string from some point about which it is allowed to swing back and forth in a place. We are asked to find the length of the physical pendulum with a known mass. Using a \(100\text{g}\) mass and \(1.0\text{m}\) ruler stick, the period of \(20\) oscillations was measured over \(5\) trials. Aim (determine a value for g using pendulum motion) To perform a first-hand investigation using simple pendulum motion to determine a value of acceleration due to the Earth's gravity (g). Using a simple pendulum, the value of g can be determined by measuring the length L and the period T. The value of T can be obtained with considerable precision by simply timing a large number of swings, but comparable precision in the length of the pendulum is not so easy. In order to minimize the uncertainty in the period, we measured the time for the pendulum to make \(20\) oscillations, and divided that time by \(20\). In this experiment the value of g, acceleration due gravity by means of compound pendulum is obtained and it is 988.384 cm per sec 2 with an error of 0.752%. 1 Objectives: The main objective of this experiment is to determine the acceleration due to gravity, g by observing the time period of an oscillating compound pendulum. We constructed the pendulum by attaching a inextensible string to a stand on one end and to a mass on the other end. Use the moment of inertia to solve for the length L: $$\begin{split} T & = 2 \pi \sqrt{\frac{I}{mgL}} = 2 \pi \sqrt{\frac{\frac{1}{3} ML^{2}}{MgL}} = 2 \pi \sqrt{\frac{L}{3g}}; \\ L & = 3g \left(\dfrac{T}{2 \pi}\right)^{2} = 3 (9.8\; m/s^{2}) \left(\dfrac{2\; s}{2 \pi}\right)^{2} = 2.98\; m \ldotp \end{split}$$, This length L is from the center of mass to the axis of rotation, which is half the length of the pendulum. Note that for a simple pendulum, the moment of inertia is I = \(\int\)r2dm = mL2 and the period reduces to T = 2\(\pi \sqrt{\frac{L}{g}}\). /Type /Page (ii) To determine radius of gyration about an axis through the center of gravity for the compound pendulum. Some of our partners may process your data as a part of their legitimate business interest without asking for consent. What should be the length of the beam? Legal. Describe how the motion of the pendulums will differ if the bobs are both displaced by 12. The angular frequency is, \[\omega = \sqrt{\frac{g}{L}} \label{15.18}\], \[T = 2 \pi \sqrt{\frac{L}{g}} \ldotp \label{15.19}\]. The restoring torque is supplied by the shearing of the string or wire. 1, is a physical pendulum composed of a metal rod 1.20 m in length, upon which are mounted a sliding metal weight W 1, a sliding wooden weight W 2, a small sliding metal cylinder w, and two sliding knife .
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determination of acceleration due to gravity by compound pendulum