Alta High Conceptual Physics Chapter 9 Circular Motion

Alta High Conceptual Physics Rotation and Revolution  Rotation – Around an internal Axis Ice skater doing a pirouette Planet rotating during one day  Revolution – around an external axis Planet going around the sun Child on the outside of a merry-go-round

Alta High Conceptual Physics Linear Speed & Rotational Speed  Linear speed is also called tangential speed – this is the definition that we have used so far this year V avg = x/t  Rotational Speed (also called angular speed) - is equal to the number of rotations per unit time ω = rotations/time = revolutions/second or radians/second

Alta High Conceptual Physics How is Tangential Speed related to Rotational Speed?  Tangential Speed = Radial Distance (radius) x rotational Speed V avg = ωR ω must be in radians – there are 2 π radians in one revolution

Alta High Conceptual Physics Sample Problems  What is the angular speed of the earth’s rotation? 1 rotation/day  What is the tangential speed of a point on the earth’s surface? V= 2 πR/day  At what speed is the earth revolving around the sun? V = 2 πR/year

Alta High Conceptual Physics Sample Problems  How many radians are in one degree? 1° (2 π radians/360°) = degrees  How many degrees are in 10 radians? 10 rad (360°/2π) = 573°  How many radians are in 3 revolutions? 3 rev (2π radians/revolution) = radians

Alta High Conceptual Physics Centripetal Acceleration Centripetal means “Center Seeking” and the centripetal force on an object moving in a circle always acts towards the center of the circle. By definition: a = V 2 /R where V = linear or tangential speed, and R is the radius of the circle.

Alta High Conceptual Physics Centripetal Force  Centripetal Acceleration results from a Centripetal Force since accelerations are always caused by outside forces Since F = ma and centripetal acceleration is a c = V 2 /R then it follows that Centripetal Force, F c = mV 2 /R

Alta High Conceptual Physics Centripetal Force  According to Newton’s 1st Law. An object in motion tends to stay in motion. It has been shown that this is straight line motion. Things want to move in straight lines, so when something is moving in a circle there must be a force causing it to stay in the circle and constantly changing the direction of its motion. Examples  When car is rounding a curve, friction between the tires and the road which is providing (not opposing) the centripetal force.  A satellite in orbit is held their by gravity (i.e. gravity is providing the centripetal force. The object actually wants to travel in a straight line, tangent to the circular path, but the provided centripetal force keeps it in a circle.

Alta High Conceptual Physics Problem Types  Conversions between revolutions, radians, and degrees  Circumference of a circle  Centripetal Acceleration  Centripetal Force