which of the following is equal to the angular acceleration of a disk?
a)first time derivative of angular position
b) second time derivative of angular position
This is comparable to the position derivatives where:
velocity = dx/dt
and
acceleration = d^2x/dt^2
The angular acceleration of a disk is equal to the second time derivative of the angular position.
To understand why, let's break it down step by step:
1. Angular position (θ): This refers to the angle at which an object, in this case, a disk, is rotating. It is generally measured in radians or degrees.
2. Angular velocity (ω): This is the rate at which the object's angular position changes with respect to time. It is the first time derivative of the angular position. Mathematically, angular velocity (ω) is represented as dθ/dt or θ̇, where dθ represents the small change in angular position and dt represents the small change in time.
3. Angular acceleration (α): This is the rate at which the angular velocity of an object changes with respect to time. It measures how quickly the object's rotation is speeding up or slowing down. It is the second time derivative of the angular position. Mathematically, angular acceleration (α) is represented as dω/dt or d²θ/dt² or θ̈, where dω represents the small change in angular velocity and dt represents the small change in time.
Therefore, the correct answer to the question is b) the second time derivative of angular position.
omega = angular VELOCITY = d Theta/ dt
alpha = angular ACCELERATION = d^2Theta/dt^2
Therefore b)