Rotational motion Objective: To determine the moment of inertia of the system by applying known torques to a system which is free to rotate, the resulting angular acceleration will ultimately measure to determine the moment of inertia of the system. Introduction:Our task in this experiment was to observe how angular velocity and radius relates to force in regard to rotational motion when dealing with rotational motion. By applying known torques to a system which is free to rotate, the resulting angular acceleration will be measured

and used to determine the moment of inertia of the system. The relationship between the net external torque and the angular acceleration is of the same form as Newton's second law and is sometimes called Newton's second law for rotation. The laws of rotational motion follow Newtons laws just as linear motion follows it. If an object is rotating about a fixed axis, then Newton’s law describing its rotational motion can be expressed as,τ=Ia(Equation 1)Where τis the net moment of force, or torque, about the axis which results in an angular acceleration, a, and I is the moment of inertiaof the object about the axis. The moment of inertiais therefore a measure of the tendency of the object to resist a change in its rotational motion, analogous to mass in linear motion. The moment of inertia of a small element of mass, m, rotating about an axis distance raway, is equivalent to mr2. The moment of inertia of an extended rigid body, depends on the way in which its mass is distributed relative to the axis of rotation. Such a body can be thought ofas made up of a very large number of elements masses and the total momentum of inertia is then the sum of contribution from all such masses. If mirepresents the mass of one such element located at a distance rifrom the axis, then the total moment of inertia can be written as:I=∑i=INmiri2(Equation 2)

If the shape of the body is simple, I can be calculated easily, but when it’s an irregular shape we can use equation 1 to find I. So, if a known torque is applied to a body and the acceleration is measured then the moment of inertia could be calculated by I=τa, our goal is to measure this method in our experiment. The apparatus comprises a heavy wooden platter with a small cylindrical spindle of radius “r” at its center. The latter is used to mount the platter on a small table and to rotate it about an axis through the center.

A cord is warped around the center spindle and passes over a pulley. When a weight of mass m is