How do you find the direction of angular acceleration?

Question

My teacher gave us this problem and i am unsure on how to solve for the direction of the angular acceleration. 

 

Mr. Foster is riding a bicycle eastward on a bicycle when he reaches a large hill and loses speed as he ascends the hill. The front wheel of his bike has a radius of 0.7 meters. If his speed decreases from 15 m/s to 5 m/s over an interval of 15 seconds, what is the direction of his angular acceleration?

Answer 1

Richard P. is correct in giving you his answer. One note I want to give you is that angular velocity and acceleration vectors are always perpendicular to the plane in which an object is rotating in. Moreover, if the angular velocity is increasing, the angular acceleration vector is pointed in the same direction as the angular velocity vector; conversely, if the angular velocity is slowing down, the angular acceleration vector would point in the opposite direction of the angular velocity vector.

 

For example, like the wheel on Mr. Foster's Bike is rotating clockwise in the x-z plane would indicate the angular velocity vector is pointed in the negative y direction, according to the right hand rule; since, the angular velocity is slowing down, the angular acceleration vector would point in the positive y direction in which is the opposite of the angular velocity vector.

Answer 2

The direction of the angular velocity vector is parallel to the axis of the wheel - so along the North South direction.

The right hand rule shows that the ω vector points to the left of Mr. Foster.  Since Mr. Forster is going East, this is the North direction.   The angular acceleration vector is anitparallel to the ω vector (because there is negative angular acceleration).   Thus the direction of the angular acceleration vector is South. 

Answer 3

Think of centripetal motion.  When you accelerate, your direction changes but the direction of velocity is tangential to acceleration.  Mr. Foster's motion is east and his speed changes as he rides up the hill.  His acceleration is due north, but because he loses speed, his direction is reversed because the force of gravity is going against his motion.  So he is actually going south.