A 6.0 kg mass in the xy plane is moving in the negative x direction at 3.0 m/s along the line y = 4.0 m.As the mass passes the point (x,y = 10 m,4.0 m),what is its angular momentum with respect to the z axis?
A) 30 SI units
B) 72 SI units
C) −60 SI units
D) −180 SI units

Question

Quizplus · Accepted Answer

The angular momentum L with respect to the z-axis is given by L = r x p, where r is the position vector measured from the z-axis and p is the momentum vector. The direction of the cross product is given by the right-hand rule.

At the point (x,y) = (10 m, 4.0 m), the position vector r is given by r = 10i + 4j, where i and j are unit vectors in the x and y directions, respectively.

The momentum vector p is given by p = mv, where m is the mass and v is the velocity vector. Since the mass is moving in the negative x-direction, the velocity vector is given by v = -3i.

Therefore, the momentum vector can be written as p = (-18 kg m/s)i.

Now, taking the cross product of r and p, we get:

L = r x p = (10i + 4j) x (-18i) = -72k

where k is the unit vector in the positive z-direction.

Thus, the magnitude of the angular momentum is 72 SI units, and its direction is opposite to the direction of motion (negative x-direction) and perpendicular to the xy-plane (positive z-direction). Therefore, the answer is (B) 72 SI units.

A 60 Kg Mass in the Xy Plane Is Moving in in the Negative