A hawk flies in a horizontal arc of radius 12.0 m at a...

A hawk flies in a horizontal arc of radius 12.0 m at a constant speed of $4.00 \mathrm{~m} / \mathrm{s}$. (a) Find its centripetal acceleration. (b) It continues to fly along the same horizontal arc but increases its speed at the rate of $1.20 \mathrm{~m} / \mathrm{s}^2$. Find the acceleration (magnitude and direction) under these conditions.

Key Concepts

Resultant Acceleration

The resultant acceleration in a situation involving both centripetal and tangential accelerations is obtained by vector addition of the two components. Since these accelerations are perpendicular to each other, the magnitude of the total acceleration is found using the Pythagorean theorem: a_total = sqrt(a_c^2 + a_t^2), and its direction can be determined using the arctan of the ratio of the tangential acceleration to the centripetal acceleration. This result gives a complete description of how the object's speed and direction are changing.

Tangential Acceleration

Tangential acceleration is the component of acceleration that is tangent to the circular path and is responsible for the change in the magnitude of the velocity (i.e., the speed). When the speed of the object increases or decreases, tangential acceleration comes into play, and its value is given by the rate of change of the speed. Unlike centripetal acceleration, it does not change the direction of velocity.

Uniform Circular Motion

Uniform circular motion refers to the movement of an object traveling at a constant speed along a circular path. Although the speed remains constant, the direction continuously changes, which implies the presence of acceleration. This concept is fundamental to understanding motions involving curves, such as orbits and rotations, where the magnitude of the acceleration may be constant and is directed towards the center of the circle.

Centripetal Acceleration

Centripetal acceleration is the acceleration that is directed towards the center of the circle in uniform circular motion. It is responsible for constantly changing the direction of the velocity vector, keeping the object moving along the curved path. The magnitude is calculated using the formula a_c = v^2 / r, where v is the speed of the object and r is the radius of the circular path.

Transcript

Please give Ace some feedback