1 / 31

310 likes | 408 Vues

Angular Momentum. Evidence of first pattern. Person in spinning chair (demo with bricks ) Rubber Stopper (demo from centripetal force lab ) Playground low tech Merry Go Round (video side F Chapter 18 ) Ice Skater (your memory) Acrobat (transparency). Informal Statement of first pattern:.

Télécharger la présentation
## Angular Momentum

**An Image/Link below is provided (as is) to download presentation**
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.
Content is provided to you AS IS for your information and personal use only.
Download presentation by click this link.
While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

**Evidence of first pattern**• Person in spinning chair (demo with bricks) • Rubber Stopper (demofrom centripetal force lab) • Playground low tech Merry Go Round (video side F Chapter 18) • Ice Skater (your memory) • Acrobat (transparency)**Informal Statement offirstpattern:**• As _ decreases, _ increases.**Informal Statement offirstpattern:**• As R decreases, _ increases.**Informal Statement offirstpattern:**• As R decreases, w increases.**Evidence of Second Pattern**• A _ _ _ _ _ _ _ _ top is stable. • A _ _ _ _ _ _ _ _ bike wheel is stable. • A gyroscope is stable when it is _ _ _ _ _ _ _ _ .**Evidence of Second Pattern**• A spinning top is stable. • A _ _ _ _ _ _ _ _ bike wheel is stable. • A gyroscope is stable when it is _ _ _ _ _ _ _ _.**Evidence of Second Pattern**• A spinning top is stable. • A spinning bike wheel is stable. • A gyroscope is stable when it is _ _ _ _ _ _ _ _ .**Evidence of Second Pattern**• A spinning top is stable. • A spinning bike wheel is stable. • A gyroscope is stable when it is spinning.**Informal Statement ofsecondpattern:**• Spinning things are more _ _ _ _ _ _ than non-spinning things. • It is tougher to change the direction of spinning things.**Informal Statement ofsecondpattern:**• Spinning things are more stable than non-spinning things. • It is tougher to change the direction of spinning things.**Formal statement(includes both patterns)**• Angular momentum: L = Iw. [ Recall: P = mv ] • If St = 0 (closed system), then L is constant. [ Recall: If SF = 0, then P is constant. ] “Conservation of Angular Momentum” • What are the units for L?**Torque and Angular Momentum**(Recall: A force can change linear momentum.) • A Torque can change angular momentum. (Recall: SF = DP / T or SF · T = DP) • St = DL / T**For the same t, the change of the L is less noticeable if**the L is large, so • Xzylo (or paper airplane shaped like a pipe) • Throw a football with a spiral. • Bikes are most stable when moving fast. • A spinning basketball can be balanced on a finger. • Tops are stable when spinning. • Gyroscopes tend to stay lined up.**Example One:Centripetal Force Apparatus**• Draw the system from the side and from the top (show the radius in both drawings). • L = Iw = Mr2w • LBEFORE = LAFTER • MR2w = Mr2w**Example Two: Playground Merry Go Round**• The person (40 kg) starts at the edge, and moves to 0.5 m from the center. • The disk is 100 kg. • The radius of the disk is 2.0 m. • Initial speed is 1 rad/s • Final speed = ?**Solve for final angular speed.**Lo = L´ person + disk = person + disk mR2w + (1/2)MR2w = mR’2w´ + (1/2)MR2w´ (40)221 + (1/2)(100)(2)21 = (40)(0.5)2w´ + (1/2)(100)(2)2w´ w´ = 1.7 rad/s (faster than before)**Closing Demonstration**• Hold spinning bicycle wheel while standing on a table that can spin. • The total angular momentum of the system is a constant. • If the person changes the L of the wheel, then the L of the person must change!!!**Rotational Energy**• Everyone would guess that a spinning object has energy, even if it’s not getting anywhere. • Kinetic or Potential? • How much? [It can’t be KE = (1/2)Mv2 , because it’s not getting anywhere.]**Build the Equation by Analogy**• Mass goes to ___ .**Build the Equation by Analogy**• Mass goes to I (rotational inertia).**Build the Equation by Analogy**• Mass goes to I. • Speed (v) goes to ___ .**Build the Equation by Analogy**• Mass goes to I. • Speed (v) goes to w (rotational speed).**Build the Equation by Analogy**• Mass goes to I. • Speed (v) goes to w (rotational speed). • KE = (1/2)Mv2 goes to KE = _____.**Build the Equation by Analogy**• Mass goes to I. • Speed (v) goes to w (rotational speed). • KE = (1/2)Mv2 goes to KE = (1/2)Iw2**Example: A Compact Disc (CD)**• How much KE does it have when it’s spinning? • KE = (1/2)Iw2 • So, what’s I and what’s w ? • Moment of Inertia for a disk = … • I = (1/2)mr2 • Mass = 16 grams (= 0.016 kg) • Radius = 6 cm (= 0.06 meter) • I = (1/2)mr2 = (1/2)(.016)(.06)2 = 0.000029 kg•m2**What else do we need?**• Get this: The disc player needs information at a constant rate, so the angular speed needs to vary! • w = {144 rotations/min 240 RPM} • w = {2.4 rotations/sec 4.0 RPS} • w = {15 radians/s 25 rad/s} • So, the average is about 20 rad/s**Finish Up: KE = (1/2)Iw2**• KE = (1/2)(.000029)(20)2 • KE = 0.0058 Joules**What is the ‘take-away’?**Just like mgh, (1/2)Mv2 , and (1/2)kx2 … rotational energy needs to be _ _ _ _ _ _ _ _ when we use an equation using energy: W = DEE2 = E1**What is the ‘take-away’?**Just like mgh, (1/2)Mv2 , and (1/2)kx2 … rotational energy needs to be included when we use an equation using energy: W = DEE2 = E1

More Related