Question

An object travels in a vertical circle of 1.41 m radius. When the object is traveling downward and is 20.5° from its lowest point, its total acceleration is a = (18.5î + 16.2ĵ) m/s2.At this instant, determine the following. (Take the angle 20.5° clockwise from the axis of the circle that intersects the center and the lowest point. Assume that the +x axis is to the right and the +y axis is up along the page.)

(a) magnitude of the radial acceleration
(b) magnitude of the tangential acceleration
(c) speed of the object
(d) velocity of the object (Express your answer in vector form.)

Answer 1

The question involves calculating various aspects of circular motion, but cannot be solved accurately without additional information about the object's dynamic properties at the given instant.

Step-by-step explanation:

The problem involves an object traveling in a circular path and requires finding various aspects of its motion such as radial acceleration, tangential acceleration, speed, and velocity. When dealing with circular motion, it's important to separate acceleration into radial (centripetal) and tangential components. The total acceleration given can be broken down into these components using trigonometry and physics principles. The radial acceleration is responsible for changing the direction of the velocity vector and is always directed towards the center of the circle. The tangential acceleration is responsible for changing the speed of the object along its path.

Unfortunately, without additional information about the object's velocity or other dynamic properties at the specified point in time, it is not possible to accurately calculate the requested values. Calculations in circular motion typically involve equations that connect angular velocity, centripetal force, and mass of the object, which are not provided in this case.