Question

A water bottle is rotating with an angular velocity of 5 radians/sec, which is the resultant of two velocities along x and y axis. then,

• A. The X-component of angular velocity is $5cos\theta$, $\theta$ is the angle between the resultant angular velocity and X axis
• B. The X-component of angular velocity is $5sin\theta$ , $\theta$ is the angle between the resultant angular velocity and X axis
• C. The Y-component of angular velocity is $5cos\theta$ , $\theta$ is the angle between the resultant angular velocity and Y axis
• D. The X-component of angular velocity is $5tan\theta$ , $\theta$ is the angle between the resultant angular velocity and X axis

Answer 1

Answer: (A), (C)

The correct options are
A The X-component of angular velocity is $5cos\theta$, $\theta$ is the angle between the resultant angular velocity and X axis
C The Y-component of angular velocity is $5cos\theta$ , $\theta$ is the angle between the resultant angular velocity and Y axis

The resultant angular velocity 5 radians/sec can be resolved in to two parts along X and Y axis.
If $\theta$ is the angle made by the resultant vector, then the X-component of angular velocity is $5cos\theta$ AND Y-component of angular velocity is $5sin\theta$