1.
You are running up a spiral staircase. The associated angular momentum points in which
direction?
a. Upwards
b. Downwards
c. The net displacement is linear, so there is no angular momentum
d. The answer cannot be determined from the information given
Angular Momentum on Spiral Staircase: Direction Analysis
Running up a spiral staircase involves helical motion, generating angular momentum whose direction follows the right-hand rule. The correct answer is option d. The answer cannot be determined from the information given, as the staircase’s rotation direction (clockwise or counterclockwise) is unspecified.
Option Breakdown
- a. Upwards: Applies if the spiral rotates counterclockwise when viewed from above, making angular momentum align upward via right-hand rule (thumb up, fingers curl counterclockwise).
- b. Downwards: Fits clockwise rotation from above, where thumb points down.
- c. The net displacement is linear, so there is no angular momentum: Incorrect; net vertical displacement occurs, but curved path around the central axis creates rotational motion and thus angular momentum
\(\vec{L} = \vec{r} \times \vec{p}\). - d. The answer cannot be determined from the information given: Correct; without knowing rotation sense (left-hand or right-hand up), direction remains ambiguous despite angular momentum existing.
Introduction to Spiral Staircase Angular Momentum
When running up a spiral staircase angular momentum direction becomes a key physics concept, blending linear and rotational motion. Helical paths generate angular momentum perpendicular to the plane of rotation, determined by the right-hand rule. This MCQ tests understanding of \(\vec{L} = I \vec{\omega}\), where direction hinges on unspecified spiral chirality.
Physics of Motion on Spiral Stairs
A person follows a helix, with position vector \(\vec{r}\) from the axis and tangential velocity \(\vec{v}\), yielding \(\vec{L} = \vec{r} \times m\vec{v}\). Spiral stairs rotate clockwise (right-hand up) or counterclockwise (left-hand up), flipping \(\vec{L}\) from up to down. Net motion is upward, but curvature ensures nonzero L.
Right-Hand Rule Application
Curl fingers along rotation; thumb gives \(\vec{L}\) direction. Counterclockwise ascent: upward \(\vec{L}\); clockwise: downward. Without rotation specified, direction cannot be fixed.
Why Option D Prevails
Options a/b assume rotation; c ignores rotation; d accounts for missing data on spiral handedness, common in exam traps. For CSIR NET prep, note angular momentum exists but vector sense needs full info.
