Centripetal acceleration and its relevance for applications of Newton’s second law

Reading Assignment 5.4: Circular motion involves A. Centripetal acceleration B. Motion in a full circle. C. Motion in equilibrium. D. Motion with a constant acceleration vector.

Circular motion at constant speed Speed? constant Velocity?Not constant Acceleration vector? Not zero Changes direction Does not change speed Must be 90° with direction of motion

Centripetal acceleration Directed toward center of curvature v a v a v a v a What can you infer about the net force on this object?

Centripetal acceleration of the Moon The Moon moves in a circle of approximately km radius. It revolves around the Earth in the time of one month, or 27d 7h 43min 12sec. Find the centripetal acceleration of the Moon. How big is the centripetal force? Which interaction provides the centripetal force?

Centripetal acceleration of the Moon In each single second: Moon is falling toward Earth but never gets there due to its forward motion

More free-body diagrams Which forces combine to provide the centripetal acceleration? In Hammer-throw, a heavy mass attached to a string is swung in a circle.

More free-body diagrams Which forces combine to provide the centripetal acceleration?

More free-body diagrams Which forces combine to provide the centripetal acceleration? The Moon is moving in a near- circle around the Earth.

In a loop-the-loop ride, the carts are upside down at the top point. Draw a force diagram, and determine the minimum speed necessary to prevent people from falling out of the cart.

More free-body diagrams Which forces combine to provide the centripetal acceleration? A car passes around a curve on a flat street.

More free-body diagrams Which forces combine to provide the centripetal acceleration? Bike racers on a banked track pass through a curve.

More free-body diagrams Which forces combine to provide the centripetal acceleration? A train passes trough a curve on a banked track.

Example flat curve A car is going around a flat curve. Assume the coefficient of static friction to be  dry =1.0 (dry road),  w =0.7 (wet road), and  i =0.3 (icy road). Determine the maximum speed at which a car can safely conquer a curve with a radius of 20 m (a typical in-town left turn on large intersection).

Example banked curve In order to minimize the dependence on friction, freeways are constructed such that large curves are banked. If a curve has a radius of 70.0 m, and cars should pass through safely at 70.0 miles per hour, find a good tilt angle for the banked curve.

You swing a ball on the end of a lightweight string in a horizontal circle at constant speed. Can the string ever be truly horizontal? If not, would it slope above the horizontal or below the horizontal? Why?

Example Marble A marble is rolling in a circle inside of a cone. The opening angle of the cone is 120º. At which speed must the marble roll for the radius of the trajectory to be 12 cm?