PHYSICS 231 INTRODUCTORY PHYSICS I Lecture 10 Last Lecture Elastic Collisions m1v1i m2v 2i m1v1 f m2v 2 f v1i v 2i v1 f v 2 f Multi part Collision Problems conserve E or p Angular motion s r in radians Angular Speed f i t t f ti in rad s Can also be given in Revolutions s Degrees s Linear tangential Speed at r s r vt t t v t r in rad s Example 7 2 A race car engine can turn at a maximum rate of 12 000 rpm revolutions per minute a What is the angular velocity in radians per second b If helicopter blades were attached to the crankshaft while it turns with this angular velocity what is the maximum radius of a blade such that the speed of the blade tips stays below the speed of sound DATA The speed of sound is 343 m s a 1256 rad s b 27 cm Angular Acceleration Denoted by f i t in rad s rad s Every point on rigid object has same and Rotational Linear Correspondence x 0 v0 f vf a t t Rotational Linear Correspondence cont d Rotational Motion Linear Motion 0 f t v0 v f x t f 0 t v f v0 at 1 2 0 t t 2 1 2 f t t 2 2 f 2 02 2 2 1 2 x v0 t at 2 1 2 x v f t at 2 2 vf v02 a x 2 2 Constant a Constant 2 Example 7 3 A pottery wheel is accelerated uniformly from rest to a rotation speed of 10 rpm in 30 seconds a What was the angular acceleration in rad s2 b How many revolutions did the wheel undergo during that time a 0 0349 rad s2 b 2 50 revolutions Linear movement of a rotating point Distance Speed s r v t r Acceleration at r Angles must be in radians Different points have different linear speeds Special Case Rolling Wheel radius r rolls without slipping Angular motion of wheel gives linear motion of car Distance x r Speed v r Acceleration a r Example 7 4 A coin of radius 1 5 cm is initially rolling with a rotational speed of 3 0 radians per second and comes to a rest after experiencing a slowing down of 0 05 rad s2 a Over what angle in radians did the coin rotate b What linear distance did the coin move a 90 rad b 135 cm Centripetal Acceleration Moving in circle at constant SPEED does not mean constant VELOCITY Centripetal acceleration results from CHANGING DIRECTION of the velocity r r v a t Acceleration points toward center of circle Derivation acent 2r v2 r v s Similar triangles v r v v s aavg t r t s arc length r Small times v a v t Using v r or v r 2 v acent 2 r r Forces Cause Centripetal Acceleration Newton s Second Law r r F ma Radial acceleration requires radial force Examples of forces Spinning ball on a string Gravity Electric forces e g atoms Example 7 5a An astronaut is in circular orbit around the Earth Which vector might describe the astronaut s velocity a Vector A b Vector B c Vector C A B C Example 7 5b An astronaut is in circular orbit around the Earth Which vector might describe the astronaut s acceleration a Vector A b Vector B c Vector C A B C Example 7 5c An astronaut is in circular orbit around the Earth Which vector might describe the gravitational force acting on the astronaut a Vector A b Vector B c Vector C A B C Example 7 6a Dale Earnhart drives 150 mph around a circular track at constant speed Neglecting air resistance which vector best describes the frictional force exerted on the tires from contact with the pavement a Vector A b Vector B c Vector C B A C Example 7 6b Dale Earnhart drives 150 mph around a circular track at constant speed Which vector best describes the frictional force Dale Earnhart experiences from the seat a Vector A b Vector B c Vector C B A C Ball on String Demo Example 7 7 A puck m 25 kg sliding on a frictionless table is attached to a string of length 0 5 m The other end of the string is fixed to a point on the table and the puck is sent revolving around the fixed point It take 2 seconds to make a complete revolution a What is the acceleration of the puck b What is the tension in the string a 4 93 m s2 b 1 23 N DEMO FLYING POKER CHIPS Example 7 8 A race car speeds around a circular track a If the coefficient of friction with the tires is 1 1 what is the maximum centripetal acceleration in g s that the race car can experience b What is the minimum circumference of the track that would permit the race car to travel at 300 km hr a 1 1 g s b 4 04 km in real life curves are banked Example 7 9 A curve with a radius of curvature of 0 5 km on a highway is banked at an angle of 20 If the highway were frictionless at what speed could a car drive without sliding off the road 42 3 m s 94 5 mph Example 7 11a Which vector represents acceleration a A b E c F d B e I Example 7 11b If car moves at design speed which vector represents the force acting on car from contact with road a D b E c G d I e J Example 7 11c If car moves slower than design speed which vector represents frictional force acting on car from contact with road neglect air resistance a B b C c E d F e I
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