2. Chapter 11 Rotational Mechanics

3. Rotational Inertia n An object rotating about an axis tends to remain rotating unless interfered with by some external influence. n This influence (rotation) is called torque. n Torque is not a force. (Torque causes rotation and Force causes acceleration.) n Torque is applied leverage.

5. Torque n Torque is the product of the force and lever- arm distance, which tends to produce rotation. Torque = force   lever arm Torque = force   lever arm »wrenches n Balanced Torque: –F x short lever arm = F x long lever arm –see-saws (Figure 11.5) or scale balances with sliding weights

6. Balanced Torque n SeeSaw - Figure 11.5 –Force x distance on each side of seesaw has to be equal. –What if the boy is 600N, how far would he have to sit from the fulcrum for equilibrium? n n 1m

7. Torque n Torque Feeler Lab n Other : “twisting forces” –Prying lid off a can with screwdriver –Turning a wrench –Opening a door –Steering wheel (modified wrench) n Consider 1) the application of a force and 2) leverage

8. Weighing an Elephant Lab (F  d) A = (F  d) B n A meter stick is suspended at its midpoint and two blocks are attached along its length. A 10-N block is attached 20cm to the left of the midpoint. Where must a 40-N block be placed in order to keep the meter stick balanced? Show your calculations

9. Torque Problems n In the previous question, if the 10-N block was changed to a 80-N block, how does the location of the 40-N block change? n To remove a nut from an old rusty bolt, you apply a 100-N force to the end of a wrench perpendicular to the wrench handle. The distance from the applied force to the axis of the bolt is 25 cm. What is the torque exerted on the bolt in N. m?

10. n Rotational Inertia http://w3.shorecrest.org/~Lisa_Peck/Physics/syllabus/mec hanics/circularmotion/hewitt/Source_Files/08_RotationalIn ertiaHam_VID.mov http://w3.shorecrest.org/~Lisa_Peck/Physics/syllabus/mec hanics/circularmotion/hewitt/Source_Files/08_RotationalIn ertiaHam_VID.mov http://w3.shorecrest.org/~Lisa_Peck/Physics/syllabus/mec hanics/circularmotion/hewitt/Source_Files/08_RotationalIn ertiaHam_VID.mov n https://www.youtube.com/watch?v=CHQOctEvtTY https://www.youtube.com/watch?v=CHQOctEvtTY

11. Rotational Inertia The greater the rotational inertia, the more difficult it is to change the rotational speed of an object. n The resistance of an object to change in its rotational motion is called rotational inertia (moment of inertia). n A torque is required to change the rotational state of motion of an object. n Rotational inertia depends on mass and how the mass is distributed. The greater the distance between the object’s mass concentration and the axis of rotation, the greater the rotational inertia. –A short pendulum has less rotation inertia and therefore swings back and forth more frequently than a long pendulum. –Bent legs swing back and forth more easily than outstretched legs.

12. Law of Rotational Inertia An object rotating about an axis tends to keep rotating about that axis in absence of an external torque. n Rotational Inertia (Moment of Inertia) is the resistance of an object to change its rotational motion. n The greater the distance of mass concentration, the greater the resistance to rotation (rotational inertia) –Balance a weight on finger –Balance a weight on long stick (similar to balancing a broom or long handled hammer) –Long legged peoples’ gaits to short peoples’ gait –Similar to adjustments needed to keep rocket vertical when first fired. –Tightrope walkers carry long poles –Training wheels on beginner bicycle

13. Formulas for Rotational Inertia n Fig. 11.14 pg.157 n Don’t memorize them. Mass more spread out the rotational inertia (I) is less.

14. Rotational Inertia & Rolling http://w3.shorecrest.org/~Lisa_Peck/Physics/syllabus/mechanics/circularmotion/hewitt/Source_Files/08_WhyABallRollsDo_VID.mov http://w3.shorecrest.org/~Lisa_Peck/Physics/syllabus/mechanics/circularmotion/hewitt/Source_Files/08_WhyABallRollsDo_VID.mov Objects of the same shape but different sizes accelerate equally when rolled down an incline. n An object with a greater rotational inertia takes more time to get rolling than an object with a smaller rotational inertia. –A hollow cylinder rolls down an incline much slower than a solid cylinder. n Shapes with greater rotational inertia (“laziness”) lag behind shapes with less rotational inertia. Greater rotational inertia is the one with its mass concentrated farther from axis of rotation. n All objects of the same shape roll down an incline with the same acceleration, even if their masses are different.

15. Rotational Inertia & Gymnastics The three principal axes of rotation in the human body are the longitudinal axis, the tranverse axis and the medial axis. n The three axes of rotation in the human body are at right angles to one another. n All three axes pass through the CG of the body. n Vertical axis that passes from head to toe is the longitudinal axis. Rotational inertia about this axis is increased by extending a leg or the arms. n Somersault or flip rotates you around your tranverse axis. Tucking in your legs and arms reduces your rotational inertia; straighten legs & arms to increase rotational inertia about this axis n Medial axis is front-to-back axis. You rotate n about the medial axis when you do a cartwheel.

16. Rotational Inertia & Gymnastics Just as the body can change shape and orientation, the rotational inertia of the body changes also. Read pg. 159-160 together. n Notice the rotational inertia about any of the axes does not depend on direction of spin. n Rotational inertia is different for the same body configuration about different axes. n US NSF - News - Science of the Olympic Winter Games - Figuring Out Figure Skating US NSF - News - Science of the Olympic Winter Games - Figuring Out Figure Skating US NSF - News - Science of the Olympic Winter Games - Figuring Out Figure Skating n US NSF - News - Science of the Olympic Winter Games - Aerial Physics (Aerial Skiing) US NSF - News - Science of the Olympic Winter Games - Aerial Physics (Aerial Skiing) US NSF - News - Science of the Olympic Winter Games - Aerial Physics (Aerial Skiing)

17. Angular Momentum Newton’s First Law of Inertia for rotating systems states that an object or system of objects will maintain its angular momentum unless acted upon by an unbalanced torque. http://w3.shorecrest.org/~Lisa_Peck/Physics/syllabus/mechanics/circularmotion/hewitt/Source_Files/08_ConservationOfAng_VID.mov n Linear momentum = mass x velocity angular momentum = rotational inertia  rotational velocity L = I  angular momentum = rotational inertia  rotational velocity L = I  n When a direction is assigned to rotational speed, it is called rotational velocity. n Angular momentum is a vector quantity and has direction as well as magnitude. I   I  I   I 

18. Angular Momentum n When an object is small compared with the radial distance to its axis of rotation, its angular momentum is equal to the magnitude of its linear momentum, mv, multiplied by the radial distance, r. angular momentum = mvr –A moving bicycle is easier to balance than a bicycle at rest because of the angular momentum provided by the spinning wheels. n If object is small compared to the radius: –I = mvr

19. Conservation of Angular Momentum n Angular momentum is conserved when no external torque acts on an object\ n A person who spins with arms extended obtains greater rotational speed when arms are drawn in. n Zero-angular-momentum twists & turns can be performed by turning one part of the body against the other. n Examples: –1. ice skater spin –2. cat dropped on back –3. diving