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Download Announcements Torque Examples of Lever Arm Example: Pedaling
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2/20/15 Announcements • Today: Torque, Angular Momentum • Wednesday: Gravity • Reading: Chapter 10, focus on figs. 10.3, 10.17, & 10.31 • Reminder: Midterm #1 is on Friday! – Topics list is posted on class website – Bring pencil, eraser, calculator, and scantron 882E Examples of Lever Arm Torque • Torque is the rotational analog of force. • Depends on: – Magnitude of Force – Direction of force – Lever arm • torque = lever arm x force • Units of N!m Example: Pedaling a Bicycle • Lever arm is amount of perpendicular distance to where the force acts. Revisiting Newton’s Laws 1: Need a linear force to change an object’s linear motion " Need a torque to change an object’s rotational motion • Equilibrium: Example: See-Saw Balancing 4m ?m – Linear: ΣF = 0 – Rotational: Στ = 0 2: Translational acceleration ~ force, and ~ 1/mass " Angular acceleration ~ torque, and ~ 1/rotational inertia 1 2/20/15 Ranking • Which meter stick requires the most torque to hold up the weight? Announcements • Today: Finish up rotation • Friday: Midterm #1! • No reading! Center of Mass Example • Average position of all the mass in an object is called the center of mass (CM) of object. • Average position of the weight distribution is called the center of gravity (CG). • When gravity is constant (usually the case), these two locations are the same. • Three trucks are parked on a slope. Which truck(s) tip over? Angular Momentum Conservation of Angular Momentum • Recall: Linear momentum = mass x velocity • Angular momentum = rotational inertia x rotational velocity If no external net torque acts on a rotating system, then the angular momentum of that system remains constant. L=Iω • Need an impulse to change linear momentum " need a torque to change angular momentum! 2 2/20/15 Examples • Conservation of angular momentum plays a big role in astronomy, because it relates tangential speed (or orbital speed) to radius (or orbital distance). • Formation of stars, planetary systems, and galaxies • Moon’s orbit around the Earth Example: Merry-go-round • What is the angular momentum of our 75 kg person going 3 m/s on the merry-goround with radius of 2 m? Angular Momentum • Special case: for an object that is small relative to its axis of rotation (planet in its orbit, bug on a turntable) Angular momentum L = mvr Units: kg m2 /s Centripetal Force • Centripetal means “towards the center.” Whenever an object moves along a circular path, there must be a force on that object in the direction of the center of the circle. • In such a case, the force is said to be centripetal Centripetal Force Example: The spin cycle! • Any force directed toward a fixed center is called a centripetal force. – Centripetal means “center-seeking” or “toward the center.” F = mv2/r r = radius of circle v = tangential velocity 3 2/20/15 Example Centrifugal Force (by XKCD) You are riding at the very edge of a merrygo-round with a radius of 2 m. Your friend runs alongside, pushing the merry-go-round so that it’s tangential speed is 3 m/s. a. What force is keeping you from sliding off? b. If you have a mass of 75 kg, what is the strength of that force? 4