Torques change angular velocity. The symbol for torque is the Greek letter τ. Torque is given by this equation:

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Moses Lindsey
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1 AP Physics Toque Foces: We ve leaned that foces change the velocity of an object. But what does it take to change the angula velocity of a thing? Well, foces ae involved, but the foce has to be applied in a special way. We call this special applied foce a toque. Thee ae many ways to apply a foce to a system that can otate. In the dawing below we have a tuntable that can spin. If we just push sideways on the thing, as in the dawing to the left, we will not make it spin. We basically would be tying to tip it ove. But if we apply a foce tangent to the disc as in the dawing to the ight, it will spin. This foce is pependicula to a adius of the cicula path. A foce that is applied pependicula to the cicula path at some distance fom the spin axis is called a toque. Toques change angula velocity. The symbol fo toque is the Geek lette τ. Toque is given by this equation: τ = F sinθ is the distance to the cente of spin fom whee the foce is applied. This vaiable is often called the leve am. F sin θ be the foce component that is pependicula to the leve am. If the angle θ is 90, then the foce is pependicula to the leve am, the sine is one, and the equation fo toque is simply: τ = F F sin θ Note fo some unknown eason, the foce is witten fist and then the leve am in this equation. θ F 196

2 You can see that the unit fo toque is going to be a newton mete (nm). We leave it like that. This looks vey simila to the unit fo wok, the joule, but it is quite diffeent. So enegy and wok ae in joules and toque is left in newton metes. Toque is a vecto quantity. 15 N is applied to a nut by a wench. The length of the wench is m. What is the toque? ( ) τ = F = 15 N m = 37.5 Nm A toque of 857 Nm is applied to flywheel that has a adius of 45.5 cm. What is the applied foce? F F τ Nm τ = = = = m N You push on the doo as shown in the dawing. What is the toque? τ = F sinθ τ = 330 N 1.5 sin55.0 ( m) 330 N τ = 410 Nm 1.5 m 55.0 Multiple Toques: What happens if two o moe toques act on an object at the same time? Two foces ae applied to the object in the dawing to the ight. The object is fee to otate about the spin axis. Both cause a toque. F 1 F 1 causes a CCW (counte clockwise) otation aound the axis. F causes a CW (clockwise) otation aound the axis. If a toque causes a clockwise otation, it is positive. spin axis 1 If a toque causes a counte clockwise otation, it is negative. F 197

3 The sum of the two toques would be: τ = τ1+ τ = F F 1 1 Equilibium and Toque:If an object is in angula equilibium (sometimes called otational equilibium), then it is eithe at est o else it is otating with a constant angula: If object is in otational equilibium, the net toque about any axis is zeo. This means that the sum of the toques acting on the object must be zeo. τ = 0 Static equilibium exists when an object has no motion, eithe linea o angula. Thee ae two conditions which must exist in ode to have you good old static equilibium: The net foce must be zeo and the net toque must be zeo. F = 0 τ = 0 This gives us some vey poweful tools to solve static poblems. We can analyze a system and look at the foces acting on it, and we can also look at the toques that act on it. We ll be able to do some eally cool stuff. Two metal obs ae attached to a vey lightweight igid wie. They ae suspended fom a igid point on the ovehead as shown. The system does not move. Calculate the distance fom the suspension line to the cente of gavity on the ight sphee. Since the system is at est, the sum of the toques and the sum of the foces must be zeo. Let s look at a FBD and a dawing showing the two toques: Without using the toque equilibium, we could not solve the poblem. The sum of foces F would simply tell us that the upwad foce would be equal to weight of the two balls. 1.0 kg 4.0 kg 45.0 cm? m g 1 m g 1 m g 1 1 m g 198

4 Using toque, howeve, allows us to solve the poblem. All we have to do is add up d toques: mg τ1 τ = 0 mg 1 1 mg = 0 mg = mg 1 1 = m g ( m) 1.0 kg 0.45 = = 0.11 m o 11cm 4.0 kg Toque poblems, as you have just seen, ae faily simple. 1 1 On aveage, we each have about 1500 deams pe yea. The only ones we emembe ae the ones inteupted by awakening and then eviewed befoe they vanish: since deams do not fom long-tem memoies (to ou knowledge), any deam not epocessed by the conscious mind is gone foeve!! Now we ll do a classic teete-totte beam poblem. A teete-totte is in equilibium as shown. The block on the left has a weight of 65 N. The beam itself has a weight of 3.5 N. What is the mass of the second block? 65 N? This is a petty simple poblem, we can solve it using the toques. The sum of the toques must be zeo: τ = 0 Thee ae thee toqes, τ 1 (fom the 65 N ock) and τ fom the othe ock. The weight of the beam (F beam ), even though it has a significant amount of weight, does not cause a toque because the weight acts at the CG of the beam which is also the cente of otation. Thus the leve am is zeo. τ + τ = 0 F + F = m 3.30 m F 1 F F beam τ is positive (CW) and τ 1 is negative (CCW) 199

5 Anothe simila poblem. ( m) F N 1.10 F 11= F F = = = 8.3 N 3.30 m To find the mass we use the second law: F kg m 1 F = ma m= = 8.3 = 3.3 kg a s m 9.8 s A 50.0 N seesaw suppots two people who weigh 455 N and 55 N. The fulcum is unde the CG of the boad. The 55 N peson is 1.50 m fom the cente. (a) Find the upwad foce n exeted by fulcum on the boad. (b) Whee does the smalle peson sit so the seesaw is balanced? 1.50 m x Fist, let s daw a FBD We know that the system is in static equilibium, so we can analyze the foces. In the y diection, the sum of the foces must be zeo. n 1 F y = 0 (a) F 1 and F ae the weight of the two men, F T is the weight of the teete-totte, and n is the nomal foce. F 1 F T F We can wite this out: n F1 F F T = 0 Now we can solve fo the nomal foce, this is the upwad foce exeted on the boad by the suppot stand. 00

6 n= F1+ F + FT = 0 = 55 N N N = 100 N (b) To find the distance the second man must be positioned fom the cente, we must analyze the toques. τ = 0 y τ + τ = 0 F + F = 0 F = F = F N ( 1.50 m) 1.73 N F = 455 N = Tivia Takes Ove: Jimmy Cate was the fist U.S. pesident to have been bon in a hospital. Eskimos use efigeatos to keep food FROM feezing. The sentence "The quick bown fox jumps ove the lazy dog." Uses evey lette in the alphabet. (developed by Westen Union to test telex/twx communications) In evey episode of Seinfeld thee is a depiction of Supeman somewhee. The aveage life span of a majo league baseball: 7 pitches. In the 1940s, the FCC assigned television's Channel 1 to mobile Sevices(two-way adios in taxicabs, fo instance) but did not Pe-numbe the othe channel assignments. That is why TV sets has channels and up, but no channel 1. The only 15 lette wod that can be spelled without epeating a lette is uncopyightable. Hang On Sloopy is the official ock song of Ohio. Did you know that thee ae coffee flavoed PEZ? The eason fiehouses have cicula staiways is fom the days of yoe when the engines wee pulled by hoses. The hoses wee stabled on the gound floo and figued out how to walk up staight staicases. The aiplane Buddy Holly died in was the "Ameican Pie." (Thus the name of the Don McLean song.) When opossums ae playing 'possum, they ae not "playing." They actually pass out fom shee teo. The Main Libay at Indiana Univesity sinks ove an inch evey yea because when it was built, enginees failed to take into account the weight of all the books that would occupy the building. The highest point in Pennsylvania is lowe than the lowest point in Coloado. Nutmeg is extemely poisonous if injected intavenously. If you have thee quates, fou dimes, and fou pennies, you have $1.19.You also have the lagest amount of money in coins without being able to make change fo a dolla. No NFL team, which plays its home games in a domed stadium, has eve won a Supebowl. The fist toilet eve seen on television was on "Leave It to Beave". The only two days of the yea in which thee ae no pofessional spots games (MLB, NBA, NHL, o NFL) ae the day befoe and the day afte the Majo League all-sta Game. Only one peson in two billion will live to be 116 o olde. The name Wendy was made up fo the book "Pete Pan." In Cleveland, Ohio, it's illegal to catch mice without a hunting license. It takes 3,000 cows to supply the NFL with enough leathe fo a yea's supply of footballs. Thee is an aveage of 178 sesame seeds on a McDonald's Big Mac bun. The wold's temites outweigh the wold's humans 10 to 1. Pound fo pound, hambuges cost moe than new cas. The 3 most valuable band names on eath: Malboo, Coca-Cola, and Budweise, in that ode. 01 When Heinz ketchup leaves the bottle, it tavels at a ate of 5 miles pe yea.

Circular Motion & Torque Test Review. The period is the amount of time it takes for an object to travel around a circular path once.

Circular Motion & Torque Test Review. The period is the amount of time it takes for an object to travel around a circular path once. Honos Physics Fall, 2016 Cicula Motion & Toque Test Review Name: M. Leonad Instuctions: Complete the following woksheet. SHOW ALL OF YOUR WORK ON A SEPARATE SHEET OF PAPER. 1. Detemine whethe each statement