Angular Displacement

Overview

Angular displacement refers to the change in the angular position of a particle moving along a circular path, measured as the angle swept by the radius connecting the particle to the center of the circle. It is a vector quantity, with its direction determined by the right-hand rule, where counterclockwise rotation is positive. Angular displacement is typically expressed in degrees, revolutions, or radians, with radians being the SI unit, defined as the ratio of the arc length to the radius of the circle. One complete revolution equals 2π radians or 360^∘.

Questions and Answers

1. What is angular displacement?

   Angular displacement is the angle swept by a particle as it moves along a circular path, measured relative to a reference axis.

2. Is angular displacement a scalar or vector quantity? Why?

   Angular displacement is a vector quantity because it has both magnitude and direction, determined by the right-hand rule.

3. How is the direction of angular displacement determined?

   The direction is determined using the right-hand rule: curl your fingers in the direction of rotation, and your thumb points in the direction of angular displacement along the axis of rotation.

4. What is the formula for the arc length of a circle in terms of angular displacement?

   The arc length is given by 𝑆 = 𝑟𝜃, where 𝑟 is the radius and 𝜃 is the angular displacement in radians.

5. When is angular displacement considered positive or negative?

   Angular displacement is positive for counterclockwise rotation and negative for clockwise rotation.

Multiple-Choice Questions

1. What is the SI unit of angular displacement?

   a) Degree
   b) Radian
   c) Revolution
   d) Meter
   Answer: b) Radian

2. Which of the following determines the direction of angular displacement?

   a) Left-hand rule
   b) Right-hand rule
   c) Fleming’s rule
   d) Axis of rotation
   Answer: b) Right-hand rule

3. For a clockwise rotation, the angular displacement is considered:

   a) Positive
   b) Negative
   c) Zero
   d) Undefined
   Answer: b) Negative

4. Which of the following is NOT a unit of angular displacement?

   a) Degree
   b) Radian
   c) Revolution
   d) Meter
   Answer: b) Meter

5. 1 radian is approximately equal to how many degrees?

   a) 180^o
   b) 57.3^o
   c) 90^o
   d) 360^o
   Answer: b) 57.3^o