The greater the applied torque, the greater the effect on the object's rate of spin. The experiment will consist of winding the string up, and then allowing the mass to fall and unwind the string. You need to double the moment of inertia added by the masses because there are two of them, as well as add the moment of inertia of the rod. The following questions need to be a part of your discussion section. From all of this, you will measure the angular acceleration, determine the moment of inertia, and check if the Law of Conservation of Energy holds in this system.
Based on this chart, which object in the following picture would you predict would reach the bottom of the incline first: the solid cylinder or the thin ring? If these numbers were incorrect, our final conclusion would be negatively affected. Introduction and Theory In this experiment, we will study the effect of a constant torque on a symmetrical body. This would then result in all other calculations to be less accurate as well. From this, we will measure its moment of inertia, which we will compare with a theoretical value. All of the rotational concepts covered are analogous to linear motion properties, with very similar equations.
In this experiment, we first set up the pulley system and tied the mass to the pulley so that, when dropped, the mass would fall over the edge of the lab table. Notice how the vectors add together. However, much was learned about relationships between different aspects of rotational motion and translational motion. Since the translational acceleration is equal to the angular acceleration times the radius, the angular acceleration is equal to the translational acceleration divided by the radius. The height that the mass reaches on its way up will be nearly the same as the starting point because energy is almost completely conserved. A Measure the distance that mass M falls from the starting point kinetic energy is zero and the potential energy is maximum to the bottom of the fall kinetic energy is maximum while the potential energy is minimum with the metric ruler provided. This is why static friction is used to calculate the torque that produces rotational motion.
We know that we obtained faulty data because our acceleration was measured to be greater than acceleration due to gravity 9. Procedure Please print the worksheet for this lab. During this, the angular velocity of the disk will increase to a maximum. Hint: Remember to find the moment of inertia of the entire rotating arm plus sliding masses. We will determine the angular acceleration of a disk. This could be due to a number of things. We probably got such problematic data because of human error, or possibly even technological error.
We taped a notecard to the mass so that it would be easier for the motion sensor to detect. Procedure Please print the worksheet for this lab. Also, from the first step of our data analysis it is easy to see the relationship between the translational acceleration of the falling mass and the angular acceleration of the pulley. Thus, if we use the average of the falling and rising α values, the effect of friction will be eliminated. Once this data was collected, we used LoggerPro software to create a more clear graph and to compute a best fit line, and, therefore, the acceleration of the mass as it was dropped from the pulley. The motion detector may have not been set up correctly, or the mass may not have been released from the pulley at the exact time needed. This could cause friction as well as the distance of rotation; again resulting in inaccurate data.
If some percent of mechanical energy has been lost, where did it get transferred to? Discuss if the graphs generated in class show the expected relationship between the physics quantities angular velocity and time. How the tire was released each time could as well. Both objects have the same mass and equal diameters. The tension can be found from an application of Newton's Second Law to this system. In this experiment, we did fulfill our purpose to measure translational acceleration, however, we did not prove that the rotational motion of the pulley was consistent with that of a disk.
Bike tires, your car's drive shaft, and the Earth itself are all examples of spinning objects. For a constant applied torque, a rotating object with smaller rotational inertia should have a greater angular acceleration than that of an object with greater rotational inertia. The apparatus for this experiment is shown in fig. If the applied torque increases, the angular acceleration should also increase. However, when the same mass is rising, the frictional and the gravitational torques are acting in the same direction.
Discussion Start your discussion with the statement of the purpose of the lab experiment, then provide a brief theoretical explanation about expected results. The only way to cause objects to spin is to apply an external torque, which is a force applied at some distance from the axis of rotation. The markers accuracy and consistency of placement could also be a factor in possible errors. Let's consider the axis of rotation passing through the disk's center of mass, cm. Energy When the mass begins to fall, the gravitational potential energy will transfer to the kinetic energy. The unit has several pulleys on it. Support all your answers with evidence.
Friction, which was not calc ulated in this experiment, would result in less than accurate time readings, the velocity, and acceleration of all trials. Was energy conserved in this experiment? Do your experimental results confirm the validity of Newton's Second Law for rotation motion? We will also study how energy is conserved in this sort of system. When the mass reaches the bottom of the string, the rotating disk will wrap the string back up until the disk has zero angular velocity. Enter the values of moment of inertia in Table 3 in the Inlab. If the tire was released with a little push, not equal to a little push in all the trials then the recorded data would not be precise. In this lab, you will measure all of these properties and thoroughly explore rotational dynamics to discover these equations. At the bottom of the object that is both rotating and translating, the contact point is instantaneously at rest.
You will need this sheet to record your data. This very well may be th e cause for the loss of energy per revolution. You have to check the Law of Conservation of Mechanical Energy using experimental data from one of the runs. How can they be reduced in the experiment? We placed the motion detector directly underneath where the mass would fall. We dropped the mass a number of times until we were able to obtain acceptable data.