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## Unit 3, Chapter 9

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**Unit 3, Chapter 9**CPO Science Foundations of Physics Chapter 9**Unit 3: Motion and Forces in 2 and 3 Dimensions**• 9.1 Torque • 9.2 Center of Mass • 9.3 Rotational Inertia Chapter 9 Torque and Rotation**Chapter 9 Objectives**• Calculate the torque created by a force. • Solve problems by balancing two torques in rotational equilibrium. • Define the center of mass of an object. • Describe a technique for finding the center of mass of an irregularly shaped object. • Calculate the moment of inertia for a mass rotating on the end of a rod. • Describe the relationship between torque, angular acceleration, and rotational inertia.**Chapter 9 Vocabulary Terms**• torque • center of mass • angular acceleration • rotational inertia • rotation • translation • center of rotation • rotational equilibrium • lever arm • center of gravity • moment of inertia • line of action**Key Question:**How does force create rotation? 9.1 Torque *Students read Section 9.1 AFTER Investigation 9.1**9.1 Torque**• A torque is an action that causes objects to rotate. • Torque is notthe same thing as force. • For rotational motion, the torqueis what is most directly related to the motion, not the force.**9.1 Torque**• Motion in which an entire object moves is called translation. • Motion in which an object spins is called rotation. • The point or line about which an object turns is its center of rotation. • An object can rotate and translate.**9.1 Torque**• Torque is created when the line of action of a force does not pass through the center of rotation. • The line of action is an imaginary line that follows the direction of a force and passes though its point of application.**9.1 Torque**• To get the maximum torque, the force should be applied in a direction that creates the greatest lever arm. • The lever arm is the perpendicular distance between the line of action of the force and the center of rotation**9.1 Torque**Lever arm length (m) t = r x F Torque (N.m) Force (N)**9.1 Calculate a torque**• A force of 50 newtons is applied to a wrench that is 30 centimeters long. • Calculate the torque if the force is applied perpendicular to the wrench so the lever arm is 30 cm.**9.1 Rotational Equilibrium**• When an object is in rotational equilibrium, the net torque applied to it is zero. • Rotational equilibrium is often used to determine unknown forces. • What are the forces (FA, FB) holding the bridge up at either end?**9.1 Calculate using equilibrium**• A boy and his cat sit on a seesaw. • The cat has a mass of 4 kg and sits 2 m from the center of rotation. • If the boy has a mass of 50 kg, where should he sit so that the see-saw will balance?**9.1 Calculate a torque**• It takes 50 newtons to loosen the bolt when the force is applied perpendicular to the wrench. • How much force would it take if the force was applied at a 30-degree angle from perpendicular? • A 20-centimeter wrench is used to loosen a bolt. • The force is applied 0.20 m from the bolt.**Key Question:**How do objects balance? 9.2 Center of Mass *Students read Section 9.2 AFTER Investigation 9.2**9.2 Center of Mass**• There are three different axes about which an object will naturally spin. • The point at which the three axes intersect is called the center of mass.**9.2 Finding the center of mass**• If an object is irregularly shaped, the center of mass can be found by spinning the object and finding the intersection of the three spin axes. • There is not always material at an object’s center of mass.**9.2 Finding the center of gravity**• The center of gravity of an irregularly shaped object can be found by suspending it from two or more points. • For very tall objects, such as skyscrapers, the acceleration due to gravity may be slightly different at points throughout the object.**9.2 Balance and center of mass**• For an object to remain upright, its center of gravity must be above its area of support. • The area of support includes the entire region surrounded by the actual supports. • An object will topple over if its center of mass is not above its area of support.**Key Question:**Does mass resist rotation the way it resists acceleration? 9.3 Rotational Inertia *Students read Section 9.3 AFTER Investigation 9.3**9.3 Rotational Inertia**• Inertia is the name for an object’s resistance to a change in its motion (or lack of motion). • Rotational inertia is the term used to describe an object’s resistance to a change in its rotational motion. • An object’s rotational inertia depends not only on the total mass, but also on the way mass is distributed.**9.3 Linear and Angular Acceleration**Angular acceleration (kg) a = a r Linear acceleration (m/sec2) Radius of motion (m)**9.3 Rotational Inertia**• To put the equation into rotational motion variables, the force is replaced by the torque about the center of rotation. • The linear acceleration is replaced by the angular acceleration.**A rotating mass on a rod can be described with variables**from linear or rotational motion. 9.3 Rotational Inertia**The product of mass × radius squared (mr2) is the**rotational inertia for a point mass where r is measured from the axis of rotation. 9.3 Rotational Inertia**The sum of mr2 for all the particles of mass in a solid is**called the moment of inertia (I). A solid object contains mass distributed at different distances from the center of rotation. Because rotational inertia depends on the square of the radius, the distribution of mass makes a big difference for solid objects. 9.3 Moment of Inertia**9.3 Moment of Inertia**The moment of inertia of some simple shapes rotated around axes that pass through their centers.**If you apply a torque to a wheel, it will spin in the**direction of the torque. The greater the torque, the greater the angular acceleration. 9.3 Rotation and Newton's 2nd Law