Rotational Motion - Lab Report Example

To demonstrate how a constant torque can create angular acceleration on a rigid body rotating about its center of mass. Background According to laws of linear motion, a stone dropped into a well covers a distance given by equation 1 below assuming the initial velocity is zero With u=0 and taking small changes in time and displacement, then the following relation holds true Considering a disk turning about some axis, equation 2 above can be converted into the angular domain as given by equation 3 below A rigid body rotates according to τ = I α.

Where,the net torque is represented by τ (given by the sum of r × F, and α =angular acceleration(rad/sec2). Recall π radian = 180 °. Take care that τ,α, and I are in consistent units. For symmetric objects the moment of inertia I is given by, where β = dimensionless fraction that lies between 0 and 1. For a rectangular block of dimensions, a × b × c has moment of inertia for a rotation about an axis normal to a × b face and passing through the center of the object.

Therefore for a rectangular block of mass M which has dimensions of a*b*c exerts a torque of τ = rT Where T is atension in the string that can be found using Newton’s second law and is given by T = m (g − a) = m (g − α r) Noting that a = α r and both g and α are positive, then a combination of all these equations yield Where we have written Id (dynamic moment of inertia) to distinguish it from the static moment of inertia I s determined from the geometry and mass.

It is also useful to look at this problem from an energy viewpoint. Thus we have Δ K + Δ U = 0 Moreover, for our specific problem this can be written as The moment of inertia is affected by the distribution of mass in the object involved and the distance of rotation from the axis of rotation. As part of our hypothesis for this lab we seek to determine whether the theoretically calculated moment of inertia corresponds to the value we obtain experimentally with all possible factors affecting it remain constant.

Methodology The mass and dimensions of the steel blockwere measured together with the errors due to measurement. The Data studio (DS) data acquisition program was opened and a file Desktop-pirtlabs-PHY 122-Rotational motion. The file was preset to record θ (t) and ω (t). The block was mounted on its shortest axis onto the rotary encoder. Precautions were taken not to tighten the screw. Part I: The blockwas attachedthrough its shortest axis onto the rotary encoder. The string was put on the mediumpulley and wind it up entirely in a direction so it will unwind CCW(counterclockwise) when facing the pulley.

  Then readings were taken. Part II: The block was mountedthrough its longest hole and Part 1 repeated and readings taken. Therefore, the dynamic moment of inertia along the short axis is greater than one for the long axis. However, the theoretically calculated static moment of inertia lies within the range defined by the dynamic moments of inertia calculated practically. It is however important to notice that the dynamic moments of inertia obtained are of the same order with Id for medium pulley through the short axis (Id = 1.66 * 10-4) being slightly higher for the long axis (Id = 1.52 * 10-4).

The moments of inertia obtained are affected by the distribution of mass from the center of mass of the object used. Thus, accurate and precise measurement of parameters that determine the moment of inertia can produce results that are close to the absolute results predicted through a theoretical approach.