A car is travelling at a constant speed v on a flat horizontal circular track of radius R . While the car is negotiating a turn to the left, a simple pendulum suspended from the roof of the car tilts away from its vertical position. What is the direction of the pendulum's tilt relative to the car, and its angle of inclination with the vertical?

Step-by-step solution

When the car takes a turn to the left, it undergoes a centripetal acceleration directed towards the center of the circular path (to the left). In the non-inertial frame of the car, a centrifugal pseudo force acts on the pendulum bob in the direction opposite to the acceleration, which is radially outward (to the right). Thus, the pendulum tilts to the right. The magnitude of the centrifugal force is F_c = mv^2 R , acting horizontally, while the gravitational force mg acts vertically downwards. At equilibrium, the a