Question

The centripetal acceleration, a(exponent sign pointing down)c, of an object moving along a circular path is proportional to the square of the object's velocity, v², and inversely proportional to the radius, r, of the circle. What kind of variation is this? Write the equation.

Answer 1

The centripetal acceleration is an example of direct variation and can be calculated using the equation a_c = v^2 / r. It is directed towards the center of rotation and increases with higher speeds and smaller radii.

Step-by-step explanation:

Centripetal Acceleration

The centripetal acceleration, ac, of an object moving along a circular path is proportional to the square of the object's velocity, v², and inversely proportional to the radius, r, of the circle. This is an example of direct variation. The equation for centripetal acceleration can be written as:

ac = v² / r

The direction of the centripetal acceleration is toward the center of rotation, which is why we give it the subscript c. It is important to note that the magnitude of centripetal acceleration increases with higher speeds and smaller radii, making it more challenging to take sharp turns at high speeds.