Suppose that a pencil is positioned so that it is vertical, with its eraser on t

Question

Suppose that a pencil is positioned so that it is vertical, with its eraser on the table. Then pencil then begins to falls to the right. The eraser experiencing sufficient friction to prevent the bottom of pencil from sliding on the table as the pencil falls.

(a) What is the direction of the pencil's angular momentum vector as it falls?

to the right

to the left

   toward the observer

away from the observer

(b) Is the pencil's angular momentum conserved during the fall?

Yes, angular momentum is conserved. No, angular momentum is not conserved because the pencil is falling with a constant rotational velocity. No, angular momentum is not conserved because friction applies a torque on the pencil.

Explanation / Answer

A) The direction of angular momentum is decided by the right-hand thumb rule. It defines that if the direction of rotation is given by the folded fingers of right hand then the thumb gives the direction of angular momentum.

Right: angular momentum is inside the plane of the paper

Left: angular momentum is outside the plane of the paper

Towards the observer: Angular momentum is on the right

Away from the observer: Angular momentum is on the left.

B)

Conservation of angular momentum is valid only in a condition of no external torque. But in the given case external torque is being applied from the bottom.

Hence: No, angular momentum is not conserved because friction applies a torque on the pencil.

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