please explain with a whole bunch of detail. I know the answers are i. -z ii. z+

Question

please explain with a whole bunch of detail. I know the answers are i. -z ii. z+ iii. -x iv. -y

4. An LP record spins clockwise, as shown, with an angular speed of 33.3 revolutions per minute. When the bug is at the location shown, give the direction of each of the following, as it slows down. Refer to the coordinate system shown, where the +z axis points out of the page. Make sure to indicate +or i. angular velocity? ii. angular acceleration? iii. tangential acceleration? iv. centripetal acceleration?

Explanation / Answer

1) Angular velocity is direction is given by RIGHT HAND rule , you just curled your fingers of right hand along the rotation then your thumb give the direction of angular velocity.

Hence here your fingers will curled in CLOCKWISE sense so your thumb will point INTO THE PAGE or -Z DIRECTION....ANSWER.

2) As wheel was rotating with some angular speed as soon as bug is seat on it's edge it's angular velocity will decrease which means a retardation is caused .

Angular acceleration will be opposite to Angular velocity then only retardation caused.

Hence direction of Angular acceleration will be in OUT OF PAGE OR Z DIRECTION.....ANSWER.

3) We know the relation between tangentially and angular acceleration

a=(alpha)×r.

So here (alpha ) means angular acceleration is along k^ and r Is along j^.

Therefore 'a' will be given by k^ × j^ = -i^ or say -X axis...ANSWER..

4) centripetal acceleration is always directed towards center so it will be along - y axis.

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