A2.0-kg block travels around a 0.40-m radius circle with an angular speed of 16 rad/s. the circle is parallel to the xy plane and is centered on the z axis, 0.60 m from the origin. what is the magnitude of the component in the xy plane of the angular momentum around the origin?

To solve this problem it is necessary to apply the concept related to the Angular Moment.

By definition the angular momentum is given as

Where

L= Angular momentum

m= mass

v= linear velocity

Recall that line speed can also be expressed as a function of angular velocity as

where is the angular velocity and R the Radius

For the case described in the statement we have that there are two distances in different components, therefore the net radius would be given by

Where

R= Radius of the block

d= displacement in z-axis

Replacing with our values we have,

Replacing in the angular momentum equation, depending on the angular velocity we have to

Therefore the magnitude of the component in the xy plane of the angular momentum around the origin is

  distance on the y-axis and time on the x-axis.

explanation:

the instantaneous velocity = change in position/time taken

the slope of the graph should give instantaneous velocity.

  slope of a graph = change in value of y -axis / change in values of x -axis

  comparing both the equations

    change in value of y -axis = change in position

  change in values of x -axis = time taken

so position values should be on the y axis and time values should be on the x axis.

distance on the y-axis and time on the x-axis.