Differences
This shows you the differences between two versions of the page.
| Both sides previous revision Previous revision Next revision | Previous revision | ||
|
phy131studiof15:lectures:chapter3 [2015/07/20 13:50] mdawber [Adding and subtracting vectors] |
phy131studiof15:lectures:chapter3 [2015/08/31 09:05] mdawber [Vectors - Components] |
||
|---|---|---|---|
| Line 25: | Line 25: | ||
| {{vectoraddsubstract.png}} | {{vectoraddsubstract.png}} | ||
| + | |||
| + | ===== 3.P.003 ===== | ||
| + | |||
| + | ===== 3.P.005 ===== | ||
| ===== Unit Vectors ===== | ===== Unit Vectors ===== | ||
| Line 60: | Line 64: | ||
| {{vectorcomponentadd.png}} | {{vectorcomponentadd.png}} | ||
| + | The angles $\theta_{1}$ and $\theta_{2}$ are defined with respect to the positive $x$ axis, ie. $\theta_{1}$ is negative and $\theta_{2}$ is positive. | ||
| | $v_{1x}=v_{1}\cos\theta_{1}$ <html>   </html> | $v_{2x}=v_{2}\cos\theta_{2}$ <html>   </html> | | | $v_{1x}=v_{1}\cos\theta_{1}$ <html>   </html> | $v_{2x}=v_{2}\cos\theta_{2}$ <html>   </html> | | ||
| Line 67: | Line 72: | ||
| | $v_{Rx}=v_{1x}+v_{2x}$ <html>   </html> | $\tan\theta_{R}=\frac{v_{Ry}}{v_{Rx}}$ <html>   </html> | | | $v_{Rx}=v_{1x}+v_{2x}$ <html>   </html> | $\tan\theta_{R}=\frac{v_{Ry}}{v_{Rx}}$ <html>   </html> | | ||
| | $v_{Ry}=v_{1y}+v_{2y}$ <html>   </html> | $v_{R}=\sqrt{v_{Rx}^2+v_{Ry}^2}$ <html>   </html> | | | $v_{Ry}=v_{1y}+v_{2y}$ <html>   </html> | $v_{R}=\sqrt{v_{Rx}^2+v_{Ry}^2}$ <html>   </html> | | ||
| + | |||
| + | ===== 3.P.027 ===== | ||
| + | |||
| + | ===== 3.P.042 ===== | ||
| + | |||
| + | ===== 3.P.051 ===== | ||
| + | |||
| + | ===== 3.P.062 ===== | ||
| + | |||
| + | |||
| + | |||
| + | |||
| + | ===== Vectors - Multiplication by a scalar ===== | ||
| + | |||
| + | Multiplication of a vector by a scalar can change the magnitude, but not the direction of the vector, ie. each component of the vector is multiplied by the scalar in the same way. | ||
| + | ===== 3.P.071 ===== | ||
