Torque. Physics 2. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

Transcription

1 Toque Physics

2 Toque Toque is what causes angula acceleation (just like a foce causes linea acceleation)

3 Toque Toque is what causes angula acceleation (just like a foce causes linea acceleation) Fo a toque to be applied to an object, thee needs to be a foce that acts at some distance away fom a pivot point. Fo example, conside tightening a bolt with a wench. Which of the 3 foces shown will tighten the bolt? Pivot Point F A F C F B

4 Toque Toque is what causes angula acceleation (just like a foce causes linea acceleation) Fo a toque to be applied to an object, thee needs to be a foce that acts at some distance away fom a pivot point. Fo example, conside tightening a bolt with a wench. Which of the 3 foces shown will tighten the bolt? Foce B will tend to otate the bolt clockwise, which will tighten it. Pivot Point F A F C F B

5 Toque Toque is what causes angula acceleation (just like a foce causes linea acceleation) Fo a toque to be applied to an object, thee needs to be a foce that acts at some distance away fom a pivot point. Fo example, conside tightening a bolt with a wench. Which of the 3 foces shown will tighten the bolt? Foce B will tend to otate the bolt clockwise, which will tighten it. Notice that foce A will tend to otate the bolt counte-clockwise, loosening it. What does foce C do? Pivot Point F A F B F C

6 Toque Toque is what causes angula acceleation (just like a foce causes linea acceleation) Fo a toque to be applied to an object, thee needs to be a foce that acts at some distance away fom a pivot point. Fo example, conside tightening a bolt with a wench. Which of the 3 foces shown will tighten the bolt? Foce B will tend to otate the bolt clockwise, which will tighten it. Notice that foce A will tend to otate the bolt counte-clockwise, loosening it. What does foce C do? Foce C doesn t cause any otation at all thee is no toque geneated by foce C. Why not? Pivot Point F A F B F C

7 Toque Toque is what causes angula acceleation (just like a foce causes linea acceleation) Fo a toque to be applied to an object, thee needs to be a foce that acts at some distance away fom a pivot point. Fo example, conside tightening a bolt with a wench. Which of the 3 foces shown will tighten the bolt? Foce B will tend to otate the bolt clockwise, which will tighten it. Notice that foce A will tend to otate the bolt counte-clockwise, loosening it. What does foce C do? Foce C doesn t cause any otation at all thee is no toque geneated by foce C. Why not? Foce C points diectly at the pivot point no toque is ceated in this case. Pivot Point F A F B F C

8 F F Toque Diection is pependicula to both adius and foce. sin( ) The angle in the fomula is between the foce and the adius (fom the pivot point to whee the foce is applied).

9 F F Toque Diection is pependicula to both adius and foce. sin( ) The angle in the fomula is between the foce and the adius (fom the pivot point to whee the foce is applied). Take a look at the diagam and θ ae shown fo foce A. Pivot Point F A θ

10 F F Toque Diection is pependicula to both adius and foce. sin( ) The angle in the fomula is between the foce and the adius (fom the pivot point to whee the foce is applied). Take a look at the diagam and θ ae shown fo foce A. Thee ae ways to intepet the fomula. If you goup the Fsin(θ) togethe, that epesents the component of the foce that is pependicula to the adius. To get the most toque, the foce should be applied pependicula (can you see why fom the fomula?) Pivot Point θ F A

11 F F Toque Diection is pependicula to both adius and foce. sin( ) The angle in the fomula is between the foce and the adius (fom the pivot point to whee the foce is applied). Take a look at the diagam and θ ae shown fo foce A. Thee ae ways to intepet the fomula. If you goup the Fsin(θ) togethe, that epesents the component of the foce that is pependicula to the adius. To get the most toque, the foce should be applied pependicula (can you see why fom the fomula?) Pivot Point θ F A The othe option is to goup the sin(θ) togethe and call it the leve am fo the foce. Think of this as the shotest distance fom the pivot point to whee the foce is applied. This is the effective adius of the foce. Again, to get maximum toque the angle should be 90.

12 Example: Find the toque of each foce shown with espect to the pivot point at the left end of the m long od. F 1 is applied at the ight end, and F is at the cente. 10 F =30N 50 F 1 =0N

13 Example: Find the toque of each foce shown with espect to the pivot point at the left end of the m long od. F 1 is applied at the ight end, and F is at the cente. 10 F =30N 50 1 (m) (0N) sin(50 ) 30.6N m F 1 =0N The diection of this toque is into the page (use the ight-hand-ule).

14 Example: Find the toque of each foce shown with espect to the pivot point at the left end of the m long od. F 1 is applied at the ight end, and F is at the cente. 10 F =30N 50 1 (m) (0N) sin(50 ) 30.6N m F 1 =0N The diection of this toque is into the page (use the ight-hand-ule). (1m) (30N) sin(10 ) 6.0N m The diection of this toque is out of the page (use the ight-hand-ule). Note that the angle could also be 60 and we get the same answe.

15 Toque We mentioned ealie that toques poduce angula acceleations. We have a fomula fo this elationship: I This is eally just Newton s nd law applied to otational motion. The moment of inetia, I, takes the place of the mass, and we use angula acceleation instead of linea.

16 Example: Find the angula acceleation of the m long, unifom od (mass=5kg) when it is subject to the foces shown. F 1 is applied at the ight end, and F is at the cente. 10 F =30N 50 F 1 =0N

17 Example: Find the angula acceleation of the m long, unifom od (mass=5kg) when it is subject to the foces shown. F 1 is applied at the ight end, and F is at the cente. 10 F =30N We will need to find the moment of inetia fo this od. Fom ou table of shapes (p.99 in textbook) we find a fomula: 50 F 1 =0N I I ML (5kg)(m) 6.67kg m

18 Example: Find the angula acceleation of the m long, unifom od (mass=5kg) when it is subject to the foces shown. F 1 is applied at the ight end, and F is at the cente. 10 F =30N We will need to find the moment of inetia fo this od. Fom ou table of shapes (p.99 in textbook) we find a fomula: 50 F 1 =0N I I ML (5kg)(m) 6.67kg m Now we can apply ou toque fomula. We ll define positive toque to mean out of the page. Altenately you can think of this as counte-clockwise. We can put a little aow symbol to indicate this in the diagam. With this choice toque 1 is negative, and toque is positive. +

19 Example: Find the angula acceleation of the m long, unifom od (mass=5kg) when it is subject to the foces shown. F 1 is applied at the ight end, and F is at the cente. 10 F =30N We will need to find the moment of inetia fo this od. Fom ou table of shapes (p.99 in textbook) we find a fomula: 50 F 1 =0N I I ML (5kg)(m) 6.67kg m Now we can apply ou toque fomula. We ll define positive toque to mean out of the page. Altenately you can think of this as counte-clockwise. We can put a little aow symbol to indicate this in the diagam. With this choice toque 1 is negative, and toque is positive. + I 30.6N 0.69 m ad s 6.0N m 6.67kg The negative sign means that the angula acceleation vecto points into the page, and the object s will acceleate in the clockwise diection. m