If a force F is applied to an object at a point Q , then the line through Q parallel to F is called the line of action of the force. We defined the vector moment of F about a point P to be P Q → × F . Show that if Q ′ is any point on the line of action of F, then P Q → × F= P Q → × F; that is, it is not essential to use the point of application to compute the vector moment—any point on the line of action will do.
If a force F is applied to an object at a point Q , then the line through Q parallel to F is called the line of action of the force. We defined the vector moment of F about a point P to be P Q → × F . Show that if Q ′ is any point on the line of action of F, then P Q → × F= P Q → × F; that is, it is not essential to use the point of application to compute the vector moment—any point on the line of action will do.
If a force F is applied to an object at a point Q, then the line through Q parallel to F is called the line of action of the force. We defined the vector moment of F about a point P to be
P
Q
→
×
F
. Show that if
Q
′
is any point on the line of action of F, then
P
Q
→
×
F=
P
Q
→
×
F;
that is, it is not essential to use the point of application to compute the vector moment—any point on the line of action will do.
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
Find the angle between vector [2, −5,7] and the x-axis
You are on a rollercoaster, and the path of your body is modeled by a vector function r(t),
where t is in seconds, the units of distance are in feet, and t = 0 represents the start of the
ride. Assume the axes represent the standard cardinal directions and elevation (x is E/W, y
is N/S, z is height). Explain what the following would represent physically, being as specific
as possible. These are all common roller coaster shapes/behaviors and can be explained in
specific language with regard to units:
a. r(0)=r(120)
b. For 0 ≤ t ≤ 30, N(t) = 0
c. r'(30) = 120
d. For 60 ≤ t ≤ 64, k(t) =
40
and z is constant.
e.
For 100 ≤ t ≤ 102, your B begins by pointing toward positive z, and does one full
rotation in the normal (NB) plane while your T remains constant.
The vector F = −a + 2a expressed in RCS and in terms of ø is
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.