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This chapter on rotational mechanics delves into the essential concepts of torque, rotational inertia, and angular momentum. It explains how torque is the force causing rotation, detailing its calculation through the product of force and lever arm. The balance of torques is illustrated through practical examples like seesaws, while the concept of center of gravity shows its influence on rotational motions. Additionally, the chapter highlights how rotational inertia affects motion and discusses angular momentum's conservation in rotating systems, crucial for understanding physical dynamics.
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Chapter 11 Rotational Mechanics
Recall: If you want an object to move, you apply a FORCE.
Similarly, If you want an object to turn or rotate, you apply a TORQUE.
Forces produce motion. Torques produce rotation.
11.1 Torque Torque is the force applied in a perpendicular fashion to an object in order to cause rotation.
11.1 Torque Torque is the product of force and the lever arm. force X lever arm (N)๋(meters)
11.1 Torque units: N๋meter (same units as work, except they are very different concepts)
11.1 Torque Lever arm – the perpendicular distance between an axis and the line of action of a force that tends to produce rotation about an axis
11.1 Torque Lever arm: The distance from the turning axis to the point of contact.
11.2 Balanced Torques a pair of torques can balance each other
11.2 Balanced Torques EX: seesaw equidistant unequal distances 200 N 200 N 200 N 400 N
11.3 Torque and Center of Gravity Center of Gravity: the point located at the object’s average position of weight
11.3 Torque and Center of Gravity Center of gravity has an effect on whether or not forces will produce rotation
11.4 Rotational Inertia Recall: Inertia – resistance to change in motion There is inertia in rotation.
11.4 Rotational Inertia rotational inertia – (also called moment of inertia) the resistance of an object to changes in its rotational motion
11.4 Rotational Inertia dependent on two things: 1. mass 2. radial distance from axis
11.4 Rotational Inertia A torque is needed to change rotational motion just as a force is needed to change linear motion.
11.4 Rotational Inertia Remember that acceleration is constant regardless of mass. Therefore the acceleration of a rolling object is not dependent on the mass of the objects.
11.4 Rotational Inertia • The less mass an object has concentrated farthest from the center of gravity, the faster it will roll since its has less rotational inertia.
11.5 Rotational Inertia and Gymnastics The human body has 3 principle axes of rotation.
11.5 Rotational Inertia and Gymnastics 1. Longitudinal axis: from head to toe least amount of inertia EX: spinning
11.5 Rotational Inertia and Gymnastics 2. Transverse axis: EX: flipping
11.5 Rotational Inertia and Gymnastics 3. Median axis: EX: cartwheel
11.6 Angular Momentum Recall: momentum is inertia of motion
11.6 Angular Momentum angular momentum: inertia of rotational motion
11.6 Angular Momentum product of rotational inertia and rotational velocity
11.6 Angular Momentum angular momentum = inertia X rotational velocity or I ๋
11.6 Angular Momentum Also, angular momentum = mvr Where m=mass v = velocity r = radius of circular path
11.6 Angular Momentum v r m
11.6 Angular Momentum Recall Newton’s First Law of Motion…
11.6 Angular Momentum For angular momentum: “An object or system of object’s will maintain its angular momentum unless acted upon by an unbalanced external torque”
11.7 Conservation of Angular Momentum Law of Conservation of Angular Momentum: “ If no unbalanced external torque acts on a rotating system, the angular momentum of that system is constant”
