Chapter 1: Vectors, Lines and Planes
Section 1.5: Applications of Vector Products
Example 1.5.13
The force is applied to the head of the position vector .
Find , the torque vector, and , its magnitude.
What is the angle between F and r?
Find a unit vector in the direction of the axis of rotation.
Solution
Mathematical Solution
Part (a)
= = =
Part (b)
= =
≐ (radians)
Part (c)
The torque vector lies along the axis of rotation.
A unit vector in this direction is
=
Figure 1.5.13(a) shows r in black, F in green, the axis of rotation as a blue line, and a unit vector along this axis in green.
Figure 1.5.13(a) Vectors r, F, and
Maple Solution - Interactive
Initialize
Tools≻Load Package: Student Multivariate Calculus
Loading Student:-MultivariateCalculus
Enter F as per Table 1.1.1.
Context Panel: Assign to a Name≻F
Enter r as per Table 1.1.1.
Context Panel: Assign to a Name≻r
Calculate , the torque vector
Common Symbols palette: Cross product operator
Display , the torque vector
Write .
Context Panel: Evaluate and Display Inline
Obtain
Keyboard the norm bars.
Write the sequence of two vectors. Context Panel: Evaluate and Display Inline
Context Panel: Student Multivariate Calculus≻Lines & Planes≻Angle
Context Panel: Approximate≻5 (digits)
Write Context Panel: Evaluate and Display Inline
Context Panel: Student Multivariate Calculus≻Normalize
Maple Solution - Coded
Install the Student MultivariateCalculus package.
Define the vectors F and r.
Apply the CrossProduct command.
Apply the Norm command.
Apply the Angle command.
Apply the evalf command.
Apply the Normalize command.
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