Phys 1 Student Workbook.pdf

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Physics Labs with Computers, Vol. 1Student WorkbookP22: Rotational Inertia 012-07000ATorque depends on the force applied and the distance from the pivot point of the rotating objectto the point where the force is applied, orτ = r × F Equation 4where r is the distance from the center of the ring or disk to the point where a force is applied(the ‘lever arm’), and F is the applied force. The value of r x F is r F sin ø where ø is theangle between r and the direction of F, the applied force. The torque is maximum when r and Fare perpendicular.In this case, the applied force is the tension (T) in a thread that is attached to a part of a rotationalapparatus. Gravity pulls a hanging mass m that is attached to the thread. The value of r is theradius of the step pulley on the apparatus. The radius is perpendicular to the applied force(Tension).Therefore, the torque is:τ = rT Equation 5The following solution is derived from the convention that up is positive and down is negative,counter-clockwise is positive and clockwise is negative.Applying Newton’s Second Law for the hanging mass, m, results in:∑ F = T − mg = m( −a)Solving for the tension in the string givesT = m( g−a)The torque is:τ = rT = rm( g −a) Equation 6The linear acceleration a of the hanging mass is the tangential acceleration, a T , of the rotatingapparatus.The angular acceleration is related to the tangential acceleration as follows:α = a T Equation 7rSubstituting Equation 6 and Equation 7 into Equation 3 gives:aI rm g a rm g a r2τTmgr 2 2⎛g ⎞= = ( − ) ÷ = ( − ) = − mr = mr ⎜ −1⎟αraT aT ⎝ aT⎠The system’s rotational inertia, I, can be calculated from the tangential acceleration, a T .For You To DoMeasure the mass and dimensions of a ring and a disk and calculate the theoretical values ofrotational inertia. Use the Rotary Motion Sensor to measure the motion of a hanging mass that isconnected by a thread to a step pulley on the rotational apparatus. Use DataStudio orScienceWorkshop to record and display velocity versus time. The slope of velocity versus time isthe tangential acceleration.p. 152 ©1999 PASCO scientific P22
Name _____________________ Class ______________ Date _________SAFETY REMINDERS• Follow directions for using the equipment.PART I: Computer Setup1. Connect the ScienceWorkshop interface to thecomputer, turn on the interface, and turn on thecomputer.2. Connect the Rotary Motion Sensor’s stereophone plugs into Digital Channels 1 and 2 on theinterface. Remove the ‘O’ ring from the largegroove on the step pulley on the sensor.3. Open the file titled as shown:500 scientificPASCOInterfacescientific300PASCOANALOG CHANNELSScienceW orkshop DATA LOGGING INSTRUCTIONSScienceWorkshopInterfaceDataStudio ScienceWorkshop (Mac) ScienceWorkshop (Win)P22 Rotational Inertia.DS (See end of activity) (See end of activity)• The DataStudio file has a Workbook display and a Graph display. Read the instructions inthe workbook.• Data recording is set at 20 Hz. The Rotary Motion Sensor is set for 360 divisions perrotation. The ‘Linear Calibration’ is set for ‘Large Groove (Pulley)’.• See the pages at the end of this activity for information about modifying aScienceWorkshop file.PART II: Sensor Calibration and Equipment Setup• You do not need to calibrate the sensor.Equipment SetupFor this part you will need the following: ring, disk, clamp-on Super Pulley, thread (all part ofthe Rotational Accessory), calipers, balance, base and support rod, Rotary Motion Sensor, masshanger.1. Complete DataTable #1 in the Lab Report section.• Measure the diameter of the large groove on the step pulley onRotary Motion Sensor. Calculate and record the radius of the steppulley.• Measure the inside and outside diameters of the ring. Calculateand record the inside radius and the outside radius of the ring.• Measure and record the radius of the disk.• Measure and record the mass of the ring and the mass of thedisk.2. Mount the Rotary Motion Sensor on a support rod so the steppulley is on top.3. Mount the clamp-on Super Pulley on the end of the RotaryMotion Sensor.P22 ©1999 PASCO scientific p. 153
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