Question

A uniform rod is fixed to a rotating turntable so that its lower end is on the axis of the turntable and it makes an angle of ${20}^0$ to the vertical. (The rod is thus rotating with uniform angular velocity about a vertical axis passing through one end.) If the turntable is rotating clockwise as seen from above.

What is the direction of the rod's angular momentum vector (calculated about its lower end) ?

• A. vertically downwards
• B. down at ${20}^0$ to the horizontal
• C. up at ${20}^0$ to the horizontal
• D. vertically upwards

Answer 1

The correct option is B down at ${20}^0$ to the horizontal

If seen from above, the disc is rotating clockwise.
Now consider any point on the rod fixed to the disc at a distance " r " from the base point.
The velocity(v) of the point considered will be perpendicular to the rod at any instant (in the direction of rotation) .
The angular momentum is given as :
$m.(r\times v)$ and is in the direction of
$(r\times v)$ which is perpendicular to the plane of r and v and on using right hand thumb rule we get the direction to be perpendicular to the base point below on the disc at an angle of 90${}^o$ from the rod which is also equal to 20${}^o$ from the disc or horizontal plane