Moment of inertia of a smart phone Introduction In this lab you will determine the moment of inertia of your phone. Two different methods are used and you will compare the results you get for each. The first method involves letting your phone fall, determining the maximum angular velocity and using mechanical energy conservation to find the moment of inertia. The second is by using a simple formula for the moment of inertia of a cuboid. Method 1: An object (fig1a) which is tilted onto one corner (fig1b) and then allowed to fall over (fig1c), will have the center of mass potential energy turned into rotational kinetic energy. (1) ? 2 = 1 2 2 The left hand side of eq1 indicates the potential energy lost as the center of mass changes height from d fig1b to c/2 (fig1c). The right hand side of eq1 is the rotational kinetic energy right before the object hits the ground. The moment of inertia is taken around the axis going through point b of the object (fig 1a). This axis goes through b directly into the paper and out of the paper. Solving eq1 for the moment of inertia around the axis passing

Preview File Edit View Go Tools Window Help 8 @ Mon Jun 10 1:22 PM E v Moment of Inertia Lab.pdf Page 1 of 2 & Q Search Introduction In this lab you will determine the moment of inertia of your phone. Two different methods are used and you will compare the results you get for each. The first method involves letting your phone fall, determining the maximum angular velocity and using mechanical energy conservation to find the moment of inertia. The second is by using a simple formula for the moment of inertia of a cuboid. 2 figure ] Method 1: An object (figla) which is tilted onto one corner (fig1b) and then allowed to fall over (figlc), will have the center of mass potential energy turned into rotational kinetic energy. (1) mgd - mg ? = 715Wmaz The left hand side of eql indicates the potential energy lost as the center of mass changes height from d fig1b to c/2 (figlc). The right hand side of eql is the rotational kinetic energy right before he object hits the ground. The moment of inertia is taken around the axis going through point b of the object (fig la). This axis goes through b directly into the paper and out of the paper. Solving eql for the moment of inertia around the axis passing through b gives: (2) 1 = mg(2d - c) Wmax Using the parallel axis theorem we can relate the moment of inertia around axis b to that around ich goes through the center of mass (point m in fig la) (3) b = ly + md So that: (4) 1 = mg(2d - c) - md2 Wmax Method 2: Alternatively the moment of inertia of a cuboid (your smart phone) around the y axis is: (5) ly = 12 m ( a2 + c ? ) . Procedure (1) Use the phyphox app gyroscope to determine the maximum angular velocity of the phone. on edge press the play button and let it fall (onto something soft!) as in figure 1. Note that in figure one, the side of the phone which is being viewed is the thin long side phone. (I have increased the thickness in the figure just to clearly show the names of the limensions). Do this five times to get an average max angular velocity. (2) Look up and/or measure the dimensions and the mass of your phone. Remember the figure is the thin long side. (3) Use the average velocity and your dimension values to find I, using equation 4. Then use the dimension values to find ly using eq5. 4) Compare the two answers. C JUN O 10 tv To