Rotational Motion and the Law of Gravity Tangential and Centripetal Motion

Rotational Motion and the Rotational Motion and the Law of GravityLaw of Gravity

Tangential and Centripetal Tangential and Centripetal MotionMotion

Relationships Between Angular and Relationships Between Angular and Linear MotionLinear Motion

Objects in circular motion have tangential Objects in circular motion have tangential speedspeed

Tangential speed – the instantaneous Tangential speed – the instantaneous linear speed of an object directed along linear speed of an object directed along the tangent to the object’s circular paththe tangent to the object’s circular path

Measured in meters/second (m/s)Measured in meters/second (m/s)

Tangential speed = radius * angular speedTangential speed = radius * angular speed

vvtt=r=rωω

Relationships Between Angular and Relationships Between Angular and Linear MotionLinear Motion

Tangential acceleration – instantaneous Tangential acceleration – instantaneous linear acceleration of an object in a circular linear acceleration of an object in a circular path tangent to the circlepath tangent to the circle

Measured in meters/secondMeasured in meters/second22 (m/s (m/s22))

Tangential acceleration = radius * angular Tangential acceleration = radius * angular accelerationacceleration

aatt = r = rαα

Centripetal AccelerationCentripetal Acceleration

Centripetal acceleration – linear Centripetal acceleration – linear acceleration directed toward the center of acceleration directed toward the center of as circular pathas circular path

Measured in meters/secondMeasured in meters/second22 (m/s (m/s22))

Centripetal acceleration = (tangential Centripetal acceleration = (tangential speed)speed)22/radius = radius * (angular speed)/radius = radius * (angular speed)22

aacc=v=vtt22/r=r/r=rωω22

Centripetal AccelerationCentripetal Acceleration

Tangential and centripetal accelerations Tangential and centripetal accelerations are perpendicularare perpendicular

Can use the Pythagorean theorem to find Can use the Pythagorean theorem to find total accelerationtotal acceleration