The pencil rotates about an axis perpendicular to the plane of the figure. which of the labeled points is the point that the axis of rotation passes through?

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The labeled points which is Letter B in the given Image is the point that the axis of rotation passes through. This problem is an example of rotational dynamics, formerly an object moves in a straight line then the motion is translational but when an object at inactivity lean towards to continue at inactivity and an object in rotation be possible to continue rotating with continuous angular velocity unless bound by a net external torque to act then is rotational. In a rotational motion, the entity is not treated as a constituent part but is treated in translational motion. It points out with the study of torque that outcomes angular accelerations of the object. 

The axis of rotation of the given pencil will pass through the point B.

Further Explanation:

Since the pencil is kept at some angle from the vertical it means that the axis of rotation of the pencil will never pass through the center of the pencil.

The weight of the pencil will act at the center of mass of the pencil whereas the normal reaction from the surface on the pencil will act at the point at which the pencil is on contact with the surface. It shows that the weight of the pencil and the normal reaction does not act along the same line.

Since the pencil is bent at some angle and it is rotating then there must be a friction force to support it on the surface.

The weight of the pencil acting at the center of mass is at some horizontal distance from the point of rotation thus, there will be a torque due to this weight about the point B and the pencil will rotate about point B.

Therefore, the axis of rotation of the given pencil will pass through the point B.

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Answer Details:

Grade: College

Subject: Physics

Chapter: Rotational Dynamics

Keywords:

Pencil rotates, axis perpendicular to plane, labeled points, axis of rotation, weight, center of mass, normal reaction, two reasonable approximations.