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GSCI 101 Chapter 8 Circular Mo5on Circular mo5on – Rota5ons – Describe the mo-on: 1)  Linear speed: the distance (meters, km, feet, ..) travelled per second (or minute or …) 2)  Rota5onal (or angular) speed: the number of rota5ons per second (or minute or …) •  33 RPM = 33 rota5ons per minute Rela5ng linear and angular descrip5ons: In one rota5on an object travels a full circle (distance 2πr) Prof. M. Nikolic, GSCI 101, Chap 8 2 Conceptual ques5on: Which moves faster? Which point moves faster? The red square. Both the same. Axis of rota5on The blue star. ✓ Need more informa5on. ★ n Prof. M. Nikolic, GSCI 101, Chap 8 3 Conceptual ques5on: Which moves faster? On a rota5ng wheel Axis of rota5on •  All points have the same rota5onal speed •  Points at larger radius have larger linear speeds ★ n Linear speed = rota-onal speed 5mes radial distance. v = ωr
The blue star has a greater linear speed than the red square. Both points have the same rota5onal speed Prof. M. Nikolic, GSCI 101, Chap 8 4 Conceptual ques5on: Rolling cup When you roll a tapered cup across a table, the path of the cup curves because the wider end rolls Slower. At the same speed. Faster. ✓ In an unexplained way. Prof. M. Nikolic, GSCI 101, Chap 8 5 Trains, wheels and turning Train wheels work similar to two fastened cups connected on wider ends. h]ps://www.youtube.com/watch?v=Wqwq1Lx0w64 Prof. M. Nikolic, GSCI 101, Chap 8 6 Rota5onal iner5a An object rotating about an axis tends to remain rotating about
the same axis at the same rotational speed unless interfered
with by some external influence.
Regular iner5a (mass): resistance to change in velocity Rota5onal iner5a (I): resistance to change in rota5onal velocity •  Depends on the amount and the distribu5on of mass •  Larger if mass is larger •  Larger if the mass is further from the center Bigger Rota5onal Iner5a I: harder to make something start rota5ng harder to make something stop rota5ng Prof. M. Nikolic, GSCI 101, Chap 8 7 Examples: Rota5onal iner5a Bigger Rota5onal Iner5a I: harder to make something start rota5ng harder to make something stop rota5ng Tight Rope Walker with a long pole. The long pole has a large rota5onal iner5a è it is harder to make him start rota5ng and fall off. Hold an object at its end è more I Hold an object at its center è less I è“choke up” on a baseball bat to lower the rota5onal iner5a and speed up the swing h]ps://www.youtube.com/watch?v=n5y5PEKy0J8 Prof. M. Nikolic, GSCI 101, Chap 8 h]p://forum.orioleshangout.com/forums/showthread.php/111696-­‐Why-­‐is-­‐
Nick-­‐choking-­‐up/page2 8 Conceptual ques5on: Rota5onal iner5a 1 Which bar (the masses are the same) is easier to twist back and forth around its center? ✓ Both the same. Need more informa5on. Prof. M. Nikolic, GSCI 101, Chap 8 9 Conceptual ques5on: Rota5onal iner5a 2 Which wheel will spin faster? Axis of rota5on Both will spin the same. Prof. M. Nikolic, GSCI 101, Chap 8 ✓ Need more informa5on. 10 Conceptual ques5on: Rota5onal iner5a 3 Which rod is easier to balance on your finger (with the heavy weight on top or on the bo]om)? ✓ Both will spin the same. Prof. M. Nikolic, GSCI 101, Chap 8 Need more informa5on. 11 Rota5onal Iner5a The rota5onal iner5a depends upon the shape of the object and its rota5onal axis. Prof. M. Nikolic, GSCI 101, Chap 8 12 Conceptual ques5on: Rota5onal iner5a 4 For round objects rolling down an incline, the fastest objects are generally those with the Greatest rota5onal iner5a compared with mass. Lowest rota5onal iner5a compared with mass. ✓ All the objects roll down with the same speed. Highest center of gravity. Prof. M. Nikolic, GSCI 101, Chap 8 13 Rota5onal Force (Torque) Archimedes of Syracuse (c. 287 BC – c. 212 BC) "Give me a lever and a place to stand and I will move the Earth." Prof. M. Nikolic, GSCI 101, Chap 8 14 Rota5onal Force (Torque) Torque = Lever arm 5mes Force Torque depends upon three factors:
•  Magnitude of the force
•  The direction in which it acts
•  The point at which it is applied on the object
Prof. M. Nikolic, GSCI 101, Chap 8 Net force changes velocity Net torque changes rota5onal velocity 15 Torque If the rota5onal speed is constant, then the net torque is zero. Net torque = clockwise torque minus counterclockwise torque Girl: CCW rota5on Torque = Force x lever = 250 N x 3 m Torque1 = 750 Nm Boy: CW rota5on Torque2 = Force x lever = Force x 1.5 m m = ?? Prof. M. Nikolic, GSCI 101, Chap 8 Balance: Torque1 = Torque2 750 Nm = Force x 1.5 m Force = 500 N m = F/g = 500 N / 10 m/s2 = 50 kg 16 Conceptual ques5on: Seesaws and Torques If this balances The lem side will rotate down Will this balance? Same weights Same horizontal distances Different ver5cal distances It will balance ✓ The right side will rotate down Need more informa5on Prof. M. Nikolic, GSCI 101, Chap 8 17 Conceptual ques5on: More torque? James cannot exert enough torque on the wrench to turn the stubborn bolt. He 5es a piece of rope to the wrench handle. Will the torque be increased if pulls equally hard on the rope as shown? Yes. Adding the rope will let him exert a lot more torque. No. Adding the rope will not let him exert a lot more torque. ✓ Need more informa5on. Prof. M. Nikolic, GSCI 101, Chap 8 18 Center of mass and center of gravity The average posi5on of the mass distribu5on. Throw a ball: it follows a smooth parabola Throw a bat: it spins and wobbles, but its center of mass follows a smooth parabola Throw a grenade: it explodes, but the center of mass of the fragments follows a smooth parabola. Prof. M. Nikolic, GSCI 101, Chap 8 19 Loca5ng the center of gravity Uniform distribu5on in the center of the object To determine the center of gravity –  suspend the object from a point and draw a ver5cal line from suspension point. –  repeat amer suspending from another point. •  The center of gravity lies where the two lines intersect. Prof. M. Nikolic, GSCI 101, Chap 8 20 Conceptual ques5on: Donut center of mass The center of mass of a donut is located: In the hole. ✓ In material making up a donut. Near but not exactly at the center of gravity. Over a point of support Applica5on: A “Fosbury flop” to clear the bar while the center of gravity passes beneath the bar Prof. M. Nikolic, GSCI 101, Chap 8 h]ps://www.youtube.com/watch?
v=RaGUW1d0w8g 21 Stability Draw a line straight down from the center of gravity •  If it falls inside the base of the object, it is in stable equilibrium •  If it falls outside the base, it is unstable. Prof. M. Nikolic, GSCI 101, Chap 8 22 Conceptual ques5on: Stability Which of these L-­‐shaped objects is stable: The one on the lem. ✓ Both are stable. CG CG The one on the right. Neither is stable. Prof. M. Nikolic, GSCI 101, Chap 8 23 Centripetal force Any force directed toward a fixed center is called a centripetal force. •  Centripetal means “center-­‐seeking” or “toward the center.” Example: To whirl a 5n can at the end of a string, you pull the string toward the center and exert a centripetal force to keep the can moving in a circle. Prof. M. Nikolic, GSCI 101, Chap 8 24 Centripetal force If the net force is zero, then objects move in straight lines. You need an inward (centripetal) force to go in a circle. Not a basic force of nature! Object Source of centripetal force Force Bike wheel Spokes Tension Whirling a ball on a String string Tension Roller coaster loop-­‐ Track the-­‐loop Normal force Moon Gravity Centripetal force needed to go in a circle: Prof. M. Nikolic, GSCI 101, Chap 8 Earth mv 2
F=
r
More force needed to go in smaller circles Much more force needed at higher speeds 25 Conceptual ques5on: Centripetal force You exit the highway on a curved ramp at the speed limit of 25 mph. The ramp needs to exert a centripetal force on your car to make it travel in a circle. If instead you exit the highway at 50 mph, then the force needed to make your car travel in a circle is: ¼ as much. ½ as much mv 2
F=
r
The same. Double. Double the speed => quadruple the force Quadrupled. ✓ Prof. M. Nikolic, GSCI 101, Chap 8 Fric5on force provides the centripetal force. 26 Conceptual ques5on: Turning car Your car turns a corner. What happens? You slide toward the door. The door moves toward you and then exerts a force on you. ✓ Normal force from the door provides the centripetal force. First Newton’s law (iner5a): Your car feels the fric5on not you! Prof. M. Nikolic, GSCI 101, Chap 8 27 Centrifugal Force •  Centrifugal means “center-­‐fleeing” or “away from the center.” Does not exist! When the car turns, the door pushes in you to make you turn also. By Newton’s 3rd Law, you push back on the door. You go in a circle (turn with the car), because of the centripetal (center seeking) force of the door on you. If you open the door – you will not move radially outward – you will just fall backwards Prof. M. Nikolic, GSCI 101, Chap 8 No force is ac5ng on you. 28 Rota5ng Reference Frame Newton’s Laws do not work here Newton’s Laws only work in reference frames traveling at constant linear velocity. Example: an airplane in straight level flight. Objects at rest stay at rest F = ma Example: an airplane in turbulence. objects at rest jump off the tray! objects spontaneously accelerate F ≠ ma Prof. M. Nikolic, GSCI 101, Chap 8 29 Simulated Gravity Stand up. You feel the normal force of the floor on your feet. You do not feel the force of gravity directly. Jump off a table. While you are falling you feel weightless. Spin the wheel. The normal force makes you go in a circle. 2
mv
For a space sta5on we want: F =
= mg
R
Prof. M. Nikolic, GSCI 101, Chap 8 30 Hollywood movies busted Star Trek: USS Enterprise – not possible 2001: A space Odyssey – possible Star Wars: Millennium falcon– not possible Prof. M. Nikolic, GSCI 101, Chap 8 31 Weightless in the ISS The Interna5onal Space Sta5on orbits the Earth every 91 minutes at a distance of 353 km above the surface of the Earth Interna5onal space sta5on does not rotate è no apparent gravity Prof. M. Nikolic, GSCI 101, Chap 8 32 Exercise: Space sta5on mv 2
F=
= mg
R
How fast does a 10-­‐m radius space sta5on need to rotate in order to feel the simulated gravity? mv 2
F=
= mg
R
v 2 = Rg
v 2 = 10m ⋅10m / s 2 = 100m 2 / s 2
v = 10
m
s
A 1-­‐km radius space sta5on? v 2 = 1000m ⋅10m / s 2 = 10000m 2 / s 2
m
v = 100
s
Prof. M. Nikolic, GSCI 101, Chap 8 Overhead 33 Angular (Rota5onal) Momentum Angular momentum = rota5onal iner5a × rota5onal velocity L = Iω (Linear momentum p = mv) No net torque çè no change in angular momentum Example: Spinning ice skater •  pulls in her arms, •  Which decreases her rota5onal iner5a (I ~ mr2) •  And increases her rota5onal velocity to compensate For small objects L = mr2ω =mvr 34 Conceptual ques5on: Rota5onal iner5a I sit on a stool holding weights in my hands and with my arms outstretched. The stool can rotate. If I bring my hands to my chest, my rota-onal iner-a (about a ver5cal axis) will Decrease. ✓ Stay the same. Increase. Need more info. Prof. M. Nikolic, GSCI 101, Chap 8 35 Conceptual ques5on: Angular momentum I sit on a stool holding weights in my hands and with my arms outstretched. The stool can rotate. If I bring my hands to my chest, my angular speed will Decrease. Stay the same. Increase. ✓ Need more info. Prof. M. Nikolic, GSCI 101, Chap 8 36 Angular Momentum Person holding rota5ng bicycle wheel on the rota5ng stool The total angular momentum of the person plus wheel plus stool is constant. The rota5onal velocity is measured around the ver5cal axis. •  Tilt the wheel so it spins clockwise •  She spins counterclockwise to compensate •  Tilt the wheel so it spins counterclockwise •  She spins clockwise to compensate 37