Question

When seen from below, the blades of a ceiling fan are seen to be revolving anticlockwise and their speed is decreasing. Select the correct statement about the direction of its angular velocity and angular acceleration.
A) Angular velocity upwards, angular acceleration downwards.
B) Angular velocity downwards, angular acceleration upwards
C) Both, angular velocity and angular acceleration upwards.
D) Both, angular velocity and angular acceleration, downwards

Answer 1

Hint : The rate of change of an object's location with regard to a frame of reference is its velocity, which is a function of time. A statement of an object's speed and direction of motion is referred to as velocity. In kinematics, the branch of classical mechanics that explains the motion of bodies, velocity is a basic notion.

Complete Step By Step Answer:
In physics, angular velocity, also known as rotational velocity or angular frequency vector, is a vector measure of rotation rate that describes how quickly an item spins or revolves relative to another point, i.e. how quickly the angular position or orientation of an item changes over time. Angular velocity may be divided into two categories. The pace at which a point object circles around a given origin, or the temporal rate at which its angular location changes relative to the origin, is referred to as orbital angular velocity. In contrast to orbital angular velocity, spin angular velocity relates to how quickly a rigid body rotates with regard to its centre of rotation and is independent of the choice of origin. The temporal rate of change of angular velocity is referred to as angular acceleration in physics. There are two forms of angular velocity: spin angular velocity and orbital angular velocity, hence there are two forms of angular acceleration: spin angular acceleration and orbital angular acceleration. The angular acceleration of a rigid body around its centre of rotation is known as spin angular acceleration, while the angular acceleration of a point particle around a fixed origin is known as orbital angular acceleration. The blades of a ceiling fan appear to be rotating anticlockwise and their speed is decreasing when viewed from below, indicating that angular velocity is operating downwards and angular acceleration is acting upwards.

Note :
The symbol alpha ($\alpha$) is used to denote angular acceleration, which is measured in units of angle per unit time squared (radians per second squared in SI units). Angular acceleration is a pseudoscalar in two dimensions, with a positive sign when the angular speed rises counterclockwise or decreases clockwise, and a negative sign when the angular speed rises clockwise or decreases counterclockwise. Angular acceleration is a pseudovector in three dimensions.