Question

1. Consider the two vectors P and Q. The definition of P is P = 􀀃i × (􀀃i × 􀀃j). The
definition of Q is Q = (􀀃i × 􀀃i) × 􀀃j .
a. The magnitude of P is equal to the magnitude of Q.
b. The magnitude of P is greater than the magnitude of Q.
c. The magnitude of P is less than the magnitude of Q.


2. We have two vectors that line in the x-y plane. If we take the cross-product of those two
vectors we know that
a. the magnitude of the cross-product will always be equal to the product of the
magnitudes of the two vectors.
b. the magnitude of the cross-product will always be greater than the product of the
magnitudes of the two vectors.
c. the magnitude of the cross-product will always be less than the product of the
magnitudes of the two vectors.
d. the cross-product vector will be perpendicular to the first vector and in the x-y
plane.
e. the cross-product vector will be in either the +z or -z direction.


3. A particle of mass 0.5 kg has velocity 2 m/s. It is moving at constant velocity along a
line that passes 0.5 m away from the origin, as shown in the figure below. Rank the
angular momentum of the particle when it is at the points A, B, and C from smallest to
greatest. Point A is 1.5 m away from the point of closest approach, B is 0.5 m away and
C is located at the point of closest approach.
a. A < B < C
b. A = B = C
c. B > C > A
d. C > B > A
e. C > A > B

4. A force, F = 5i􀀃 is applied at a point located at a position of R = 2i􀀃 + 4j􀀃 . What
torque does this force exert relative to the origin?
a. 5 Nm in the + x-direction
b. 5 Nm in the + z-direction.
c. 10 Nm in the - x-direction
d. 10 Nm in the - z-direction.
e. 20 Nm in the + x-direction

Answer 1

No homework dumping please.

Show some work for assistance. Post one long question at a time.

Answer 2

1. I am thinking A since the vectors are techinqually the same and multiplication is associative
2. I am pretty sure it is E.
3.since the particle is not attached/drawn to the origin i believe it has no angular momentum and therefore B
4. 5 times 2 is 10 so C or D so I am thinking C

Answer 3

4. Torque is the cross product of F and R vectors. It must be in the z (k vector) direction since F and R are in the x-y plane. I would expect the answer to be 20 N*m in the +z direction.

Did you type choice e. direction correctly?

I do not understand the meaning of your square symbols &#56256;&#56323;.

Answer 4

the square was is the ^ on top of the i and j vectors.

also does that mean 1-3 is correct?

Answer 5

I did not answer 1-3. I suggest you post them separately for someone else to answer

Answer 6

I did check E and it is 20NM in the -Z
So now I am even more confused.

Answer 7

The +/- sign depends upon whether the torque is defined by R x F or F x R. Perhaps I got the order wrong.

E is the right answer.

Answer 8

20 in -z direction (-20 k) is correct

R x F

i j k
2 4 0
5 0 0

= - 20 k

Answer 9

I had torque as F x R, nor R x F.
Forgot which it is.
Hence the sign change.