In order to change the angular momentum of an object, it is necessary to apply
a. a net force to the object.
b. a net torque to the object.
c. a centripetal acceleration to the object.
d. both a net force and a net torque to the object.
We have three vectors, labeled A, B, and C. A points due west, B points due north, and C points due east. We don’t know their relative magnitudes. We find the cross product of each of these vectors with a vector which points due south (D). Rank the three cross products ( ) from smallest to largest in terms of their vertical component, taking the sign of the component into account.
g. You cannot tell with the given information
To change angular momentum requires a moment(torque)
LOL, yes you can tell
first B X D
the angle between B and D is 180, and the sine of 180 is zero
therefore B X D = 0
that was easy
Now A X D
rotation from A to D is + 90 degrees, so A X D is UP, positive
But C X D
rotation from C to D is negative 90 degrees, cross product down
C X D is DOWN, negative
Thus
in order
CXD negative
BXD zero
AXD positive
O-O
To answer the first question about changing the angular momentum of an object, we can refer to the basic principles of rotational motion. Angular momentum is a property of rotating or moving objects, and it depends on both the mass and distribution of mass within the object and its rotation speed. The rate of change of angular momentum can be achieved by applying a net torque to the object.
Therefore, the correct answer to the question is b. a net torque to the object.
For the second question regarding the cross products of vectors A, B, and C with a vector D, we can determine the relative sizes of their vertical components by considering the directions of the vectors and the right-hand rule. Since vector A points due west and vector D points due south, their cross product would produce a vector that points upwards, with its vertical component being positive. Similarly, since vector C points due east and vector D points due south, their cross product would also produce a vector that points upwards, with its vertical component being positive.
On the other hand, vector B points due north, and when crossed with vector D, the resulting vector would point downwards, with its vertical component being negative.
Hence, we can rank the three cross products from smallest to largest in terms of their vertical component, taking the sign of the component into account, as follows:
1. B × D (smallest, negative vertical component)
2. A × D
3. C × D (largest, positive vertical component)
Therefore, the correct answer is: g. You cannot tell with the given information.