What is centripetal acceleration? What is the direction of the centripetal acceleration of a car going around a curve?

Centripetal acceleration is the rate of change of an object's velocity as it moves in a circular path. It is always directed towards the center of the circle and is perpendicular to the object's velocity. The formula for centripetal acceleration is given by: \[a_c=\frac{v^2}{r}\] where \(a_c\) is the centripetal acceleration, \(v\) is the object's velocity, and \(r\) is the radius of the circular path.

To determine the direction of the centripetal acceleration of a car going around a curve, imagine the car moving in a clockwise direction along the curve. As the car moves along the curve, its velocity vector constantly changes, pointing tangent to the circular path at every point. However, the centripetal acceleration is always directed towards the center of the circle, which is perpendicular to the car's velocity. Let's take a specific example: if the car is moving along a curve in a circular path, and the car is at the top of the circle: - The velocity of the car will be directed horizontally to the right (tangent to the circular path). - The centripetal acceleration of the car will be directed vertically downwards, towards the center of the circle (perpendicular to the velocity). If the car is at the bottom of the circle: - The velocity of the car will be directed horizontally to the left (tangent to the circular path). - The centripetal acceleration of the car will be directed vertically upwards, towards the center of the circle (perpendicular to the velocity). In both cases, the centripetal acceleration is always directed towards the center of the circular path.