SMU PHYSICS 1303: Introduction to Mechanics Stephen Sekula1 1Southern Methodist University Dallas, TX, USA SPRING, 2019 S. Sekula (SMU) SMU — PHYS 1303 SPRING, 2019 1 Outline Rotational Energy and Force Concepts S. Sekula (SMU) SMU — PHYS 1303 SPRING, 2019 2 Rotational Energy and Force Concepts Rotational Energy and Force Concepts “Jet Engine” by William Warby, available via Creative Commons from Flickr S. Sekula (SMU) SMU — PHYS 1303 SPRING, 2019 3 Rotational Energy and Force Concepts Key Ideas The key ideas that we will explore in this section of the course are as follows: I We will begin to think about energy and force concepts as they relate to extended, rigid, rotating bodies. I We will see that there are rotational analogs to linear concepts, like kinetic energy. “Sprunger Table Saw blade” by I We will come to understand how forces result in rotations, and lungstruck, available under Creative explore the concept of a torque. Commons from Flickr I We will connect the force and energy concepts through work, and complete a set of rotational analogs to linear energy and force concepts. S. Sekula (SMU) SMU — PHYS 1303 SPRING, 2019 4 Rotational Energy and Force Concepts Key Ideas The key ideas that we will explore in this section of the course are as follows: I We will begin to think about energy and force concepts as they relate to extended, rigid, rotating bodies. I We will see that there are rotational analogs to linear concepts, like kinetic energy. “Sprunger Table Saw blade” by I We will come to understand how forces result in rotations, and lungstruck, available under Creative explore the concept of a torque. Commons from Flickr I We will connect the force and energy concepts through work, and complete a set of rotational analogs to linear energy and force concepts. S. Sekula (SMU) SMU — PHYS 1303 SPRING, 2019 4 Rotational Energy and Force Concepts Key Ideas The key ideas that we will explore in this section of the course are as follows: I We will begin to think about energy and force concepts as they relate to extended, rigid, rotating bodies. I We will see that there are rotational analogs to linear concepts, like kinetic energy. “Sprunger Table Saw blade” by I We will come to understand how forces result in rotations, and lungstruck, available under Creative explore the concept of a torque. Commons from Flickr I We will connect the force and energy concepts through work, and complete a set of rotational analogs to linear energy and force concepts. S. Sekula (SMU) SMU — PHYS 1303 SPRING, 2019 4 Rotational Energy and Force Concepts Key Ideas The key ideas that we will explore in this section of the course are as follows: I We will begin to think about energy and force concepts as they relate to extended, rigid, rotating bodies. I We will see that there are rotational analogs to linear concepts, like kinetic energy. “Sprunger Table Saw blade” by I We will come to understand how forces result in rotations, and lungstruck, available under Creative explore the concept of a torque. Commons from Flickr I We will connect the force and energy concepts through work, and complete a set of rotational analogs to linear energy and force concepts. S. Sekula (SMU) SMU — PHYS 1303 SPRING, 2019 4 Rotational Energy and Force Concepts Key Ideas The key ideas that we will explore in this section of the course are as follows: I We will begin to think about energy and force concepts as they relate to extended, rigid, rotating bodies. I We will see that there are rotational analogs to linear concepts, like kinetic energy. “Sprunger Table Saw blade” by I We will come to understand how forces result in rotations, and lungstruck, available under Creative explore the concept of a torque. Commons from Flickr I We will connect the force and energy concepts through work, and complete a set of rotational analogs to linear energy and force concepts. S. Sekula (SMU) SMU — PHYS 1303 SPRING, 2019 4 Rotational Energy and Force Concepts The Kinetic Energy of a Rotating Body Let me begin with a question: I am going to throw the vent fan pictured left at your hand at a linear speed of 170km/h. Is that okay? To which you probably replied: ‘No. That is highly unsafe.” Why? Because this giant vent fan would have a huge linear kinetic energy, part of which would be transferred to you either in an elastic or inelastic collision. That will hurt. A LOT. “Giant Ventilation Fan” by Christoper and available under Creative Commons from Flickr S. Sekula (SMU) SMU — PHYS 1303 SPRING, 2019 5 Rotational Energy and Force Concepts The Kinetic Energy of a Rotating Body Let me begin with a question: I am going to throw the vent fan pictured left at your hand at a linear speed of 170km/h. Is that okay? To which you probably replied: ‘No. That is highly unsafe.” Why? Because this giant vent fan would have a huge linear kinetic energy, part of which would be transferred to you either in an elastic or inelastic collision. That will hurt. A LOT. “Giant Ventilation Fan” by Christoper and available under Creative Commons from Flickr S. Sekula (SMU) SMU — PHYS 1303 SPRING, 2019 5 Rotational Energy and Force Concepts The Kinetic Energy of a Rotating Body Let me begin with a question: I am going to throw the vent fan pictured left at your hand at a linear speed of 170km/h. Is that okay? To which you probably replied: ‘No. That is highly unsafe.” Why? Because this giant vent fan would have a huge linear kinetic energy, part of which would be transferred to you either in an elastic or inelastic collision. That will hurt. A LOT. “Giant Ventilation Fan” by Christoper and available under Creative Commons from Flickr S. Sekula (SMU) SMU — PHYS 1303 SPRING, 2019 5 Rotational Energy and Force Concepts The Kinetic Energy of a Rotating Body Let me begin with a question: I am going to throw the vent fan pictured left at your hand at a linear speed of 170km/h. Is that okay? To which you probably replied: ‘No. That is highly unsafe.” Why? Because this giant vent fan would have a huge linear kinetic energy, part of which would be transferred to you either in an elastic or inelastic collision. That will hurt. A LOT. “Giant Ventilation Fan” by Christoper and available under Creative Commons from Flickr S. Sekula (SMU) SMU — PHYS 1303 SPRING, 2019 5 Rotational Energy and Force Concepts The Kinetic Energy of a Rotating Body Fine. Let me ask a different question: The vent fan has a uniform distribution of mass, so its center of mass (COM) is located dead center — just on its axis of rotation. I’m going to spin the fan so the tip of its blades move at 170km/h. But since the COM is still, it has no linear kinetic energy. I’m going to stick your hand into the path of the blades. Is that okay? To which you probably replied: ‘HECK no. That is highly unsafe.” Why? Because even though it’s “Giant Ventilation Fan” by Christoper and true that the COM has no linear kinetic energy, available under Creative Commons from Flickr those blades are moving, and there is clearly some kind of kinetic energy associated with rotation. Let’s figure out what that is. S. Sekula (SMU) SMU — PHYS 1303 SPRING, 2019 6 Rotational Energy and Force Concepts The Kinetic Energy of a Rotating Body Fine. Let me ask a different question: The vent fan has a uniform distribution of mass, so its center of mass (COM) is located dead center — just on its axis of rotation. I’m going to spin the fan so the tip of its blades move at 170km/h. But since the COM is still, it has no linear kinetic energy. I’m going to stick your hand into the path of the blades. Is that okay? To which you probably replied: ‘HECK no. That is highly unsafe.” Why? Because even though it’s “Giant Ventilation Fan” by Christoper and true that the COM has no linear kinetic energy, available under Creative Commons from Flickr those blades are moving, and there is clearly some kind of kinetic energy associated with rotation. Let’s figure out what that is. S. Sekula (SMU) SMU — PHYS 1303 SPRING, 2019 6 Rotational Energy and Force Concepts The Kinetic Energy of a Rotating Body Fine. Let me ask a different question: The vent fan has a uniform distribution of mass, so its center of mass (COM) is located dead center — just on its axis of rotation. I’m going to spin the fan so the tip of its blades move at 170km/h. But since the COM is still, it has no linear kinetic energy. I’m going to stick your hand into the path of the blades. Is that okay? To which you probably replied: ‘HECK no. That is highly unsafe.” Why? Because even though it’s “Giant Ventilation Fan” by Christoper and true that the COM has no linear kinetic energy, available under Creative Commons from Flickr those blades are moving, and there is clearly some kind of kinetic energy associated with rotation. Let’s figure out what that is. S. Sekula (SMU) SMU — PHYS 1303 SPRING, 2019 6 Rotational Energy and Force Concepts The Kinetic Energy of a Rotating Body Fine. Let me ask a different question: The vent fan has a uniform distribution of mass, so its center of mass (COM) is located dead center — just on its axis of rotation.