Objective: The purpose of this experiment is to test the validity of Newton's 2nd Law as it applies to the case of an object moving with constant speed in a circular path and, therefore, being acted on by a centripetal force. Apparatus: EXPERIMENT 6 UNIFORM CIRCULAR MOTION Self-contained Uniform Circular Motion (UCM) unit, mass suspended from strings, spring attached to multihole ladder, weights, timer clock. Theory: Uniform Circular Motion describes the motion of object that moves along a circular path with velocity v whose magnitude is constant. The direction of the velocity changes, of course, as the object moves along the circular path and, being always tangent to the path, it is always perpendicular to the radius of the circle. When this occurs, we can show that the object has an acceleration that is constant in magnitude and always pointing along the radius toward the center of the circular path. For this reason, the acceleration in UCM is called "centripetal acceleration" acp. Its (constant) magnitude is given by: acp=v²/R (1) where R is the radius of the circle. In this case, recalling Newton's 2nd Law of Motion F = ma, the net external force F acting on the object must also point toward the center of the circle, as its direction is always parallel to the acceleration. For this reason the net external force in UCM is called "centripetal force" Fcp. Therefore, we rewrite Newton's 2nd Law for UCM as: Fcp = macp = m v²/R (2) R V m For the purposes of this experiment it is useful to further rewrite (2), by noting that the speed v can be written in terms of the radius R and frequency f of the circular motion. The frequency f is the number of revolutions per second, which is the inverse of the period T of the motion, the time required for the object to go around once). Recall v= distance/time = circumference/period = 2лR/T = 2лRf. Therefore, Eqn. (2) can be rewritten as: Fcp = 4π²mRf² (3) Note: If the values of m and R are fixed, Egn. (3) is the equation of a straight line where Fcp is the dependent variable, f2 is the independent variable and 4²mR is the slope (recall y = constant-x). This equation gives the theoretical prediction for the centripetal force and is the equation that actually will be tested in this experiment.

Objective: The purpose of this experiment is to test the validity of Newton's 2nd Law as it applies to the case of an object moving with constant speed in a circular path and, therefore, being acted on by a centripetal force. Apparatus: EXPERIMENT 6 UNIFORM CIRCULAR MOTION Self-contained Uniform Circular Motion (UCM) unit, mass suspended from strings, spring attached to multihole ladder, weights, timer clock. Theory: Uniform Circular Motion describes the motion of object that moves along a circular path with velocity v whose magnitude is constant. The direction of the velocity changes, of course, as the object moves along the circular path and, being always tangent to the path, it is always perpendicular to the radius of the circle. When this occurs, we can show that the object has an acceleration that is constant in magnitude and always pointing along the radius toward the center of the circular path. For this reason, the acceleration in UCM is called "centripetal acceleration" acp. Its (constant) magnitude is given by: acp=v²/R (1) where R is the radius of the circle. In this case, recalling Newton's 2nd Law of Motion F = ma, the net external force F acting on the object must also point toward the center of the circle, as its direction is always parallel to the acceleration. For this reason the net external force in UCM is called "centripetal force" Fcp. Therefore, we rewrite Newton's 2nd Law for UCM as: Fcp = macp = m v²/R (2) R V m For the purposes of this experiment it is useful to further rewrite (2), by noting that the speed v can be written in terms of the radius R and frequency f of the circular motion. The frequency f is the number of revolutions per second, which is the inverse of the period T of the motion, the time required for the object to go around once). Recall v= distance/time = circumference/period = 2лR/T = 2лRf. Therefore, Eqn. (2) can be rewritten as: Fcp = 4π²mRf² (3) Note: If the values of m and R are fixed, Egn. (3) is the equation of a straight line where Fcp is the dependent variable, f2 is the independent variable and 4²mR is the slope (recall y = constant-x). This equation gives the theoretical prediction for the centripetal force and is the equation that actually will be tested in this experiment.