As a 2.0-kg block travels around a 0.50-m radius circle with an angular speed of 12 rad/s. The circle is parallel to the xy plane and is centered on the z axis, a distance of 0.75 m from the origin. The z component of the angular momentum around the origin is: A) 6.0 kg.m²/s B) 9.0 kg . m²/s C) 11 kg . m²/s D) 14 kg . m²/s E) 20 kg . m²/s

Question

Quizplus · Accepted Answer

The z component of the angular momentum is given by:$$L_z = I_z \omega_z$$where:$$I_z$$ is the moment of inertia about the z-axis$$\omega_z$$ is the angular velocity about the z-axisIn this case, the moment of inertia about the z-axis is:$$I_z = mr^2$$where:$$m$$ is the mass of the block$$r$$ is the radius of the circleThe angular velocity about the z-axis is:$$\omega_z = \omega$$where:$$\omega$$ is the angular speedSubstituting these values into the equation for the z component of the angular momentum, we get:$$L_z = mr^2 \omega$$$$L_z = (2.0 	ext{ kg})(0.50 	ext{ m})^2(12 	ext{ rad/s})$$$$L_z = 6.0 	ext{ kg m}^2/	ext{s}$$Therefore, the correct answer is A.

As a 20-Kg Block Travels Around a 0