Final answer:
To calculate the acceleration of point A with a given velocity on a rotating disk, you can use centripetal acceleration (ac = v2/r). If the point also experiences tangential acceleration, then the total acceleration can be calculated by combining both tangential and centripetal components.
Step-by-step explanation:
Calculating the Acceleration of Point A in Circular Motion
In circular motion, the velocity vector of a point on a rotating disk changes direction at every instant, generating centripetal acceleration, which always points towards the center of the circle. This means that even if the magnitude of the speed does not change, the changing direction implies an acceleration. When you are given the speed (not the velocity) of a point on a disk, you know the speed at the point is tangential to the circle, and thus you can calculate the centripetal acceleration using the formula:
ac = v2/r
Here, v is the speed of the point and r is the radius of the circular path. If the point is also experiencing tangential acceleration due to the change in the magnitude of velocity over time, then the total acceleration can be found using vector addition of tangential and centripetal accelerations:
total acceleration = √(at2 + ac2)
If only the centripetal acceleration is considered (assuming no tangential acceleration), then for point A with a velocity of 8 ft/s and radius r, its centripetal acceleration can be given as ac = (8 ft/s)2/r.
Tangential acceleration is also present when the speed of the object is changing as a result of a non-zero angular acceleration. In the case where the tangential acceleration of another point, B, is given as 9 ft/s2, we can infer angular acceleration of the disk (not directly asked in the question).