Question

in which direction the angular velocity of the earth point?
east
west
south
north
the earth day has been lengthening over a long period of time. in what direction does its angular acceleration vector point?
east
south
north
west

Explanation:

• For the first question: The right - hand rule is used to determine the direction of angular velocity. If we curl the fingers of our right hand in the direction of the Earth's rotation (from west to east), the thumb points in the direction of the angular velocity vector. The Earth rotates from west to east, and by the right - hand rule, the angular velocity vector points along the Earth's axis of rotation, which is towards the North.
• For the second question: Since the length of the Earth's day is increasing, the angular velocity \(\omega\) of the Earth is decreasing (\(\omega=\frac{2\pi}{T}\), where \(T\) is the period of rotation, and as \(T\) increases, \(\omega\) decreases). The angular acceleration \(\alpha=\frac{d\omega}{dt}\). Since \(\omega\) (which is in the north - direction as established above) is decreasing, the angular acceleration \(\alpha\) is in the opposite direction of \(\omega\), so it points towards the South.

Answer:

• First question: North
• Second question: South