KIN 3309 1st Edition Lecture 20 Outline of Last Lecture I Torque II Levers III Rotational Analog of Newton s First Law IV Moment of Inertia V Angular Momentum VI Rotational Analog of Newton s Second Law VII Rotational Analog of Newton s Third Law VIII Conservation of Angular Momentum IX Outline X Centers of Mass Gravity XI Total Body Center of Mass XII Linear vs Angular Kinetic Analysis XIII Dynamic Analysis XIV Angular Impulse XV Angular Work XVI Angular Power XVII Angular Energy XVIII Work Energy Theorem These notes represent a detailed interpretation of the professor s lecture GradeBuddy is best used as a supplement to your own notes not as a substitute XIX Quiz Outline of Current Lecture I How to Solve Biomechanics Problems II Question 1 III Angular and Linear Velocity IV Question 2 V Question 3 VI Question 4 VII Linear vs Angular Kinetic Analysis VIII Question 5 IX Question 6 X Conservation of Angular Momentum XI Question 7 XII Angular Impulse XIII Question 8 XIV Question 9 XV Question 10 Current Lecture I How to Solve Biomechanics Problems a Step 1 i Identify clearly what the problem is asking b Step 2 i Identify the information you are given c Step 3 i Identify relationships d Step 4 i Combine the given information and the relationships II Question 1 a During the delivery phase of fastball pitch the arm internally rotates at the shoulder The angular velocity of this internal rotation peaks at 120 rad s At this instant the elbow angle is 90 degrees so the angular velocity of the forearm is also 120 rad s The baseball in the pitcher s hand is 35 cm from this axis of rotation through the shoulder joint At this instant the linear velocity of the baseball is 45 m s i A How much of the baseball s total linear velocity is due to the 120 rad s angular velocity of the forearm 1 93 ii B What is the centripetal acceleration of the baseball at this instant in m s2 1 5040 m s2 iii C How large is the force exerted by the pitcher on the baseball to cause this acceleration The baseball s mass is 145 g 1 731 N III Angular and Linear Velocity a The linear velocity can be determined when the length of the segment radius and the angular velocity are known IV Question 2 a A person wants to push an 110 kg box across the floor The coefficient of friction between the box and the floor is 0 3 i A What is the normal force experienced by the box as it sits on the floor 1 1079 1 N ii B If the person pushes horizontally on the box how much force must be applied to move the box 1 F 323 73 N iii C If the person pushes against the box with the force calculated in b but at an angle of 20 degrees relative to the horizontal what is the normal force experienced by the box 1 1189 82 N V Question 3 a A 608 N women dives from a 10 m platform No external forces are applied during diving No external forces are applied during diving i A What is her potential and kinetic energy 7 m into the dive 1 KE 4256 Nm 2 PE 1824 Nm ii B What is her linear velocity 7 m into the dive 1 v 11 72 m s VI Question 4 a An athlete is doing a knee extension exercise using a 140 N dumbbell strapped to her ankle 37 cm from the knee joint The athlete holds her leg so that the horizontal distance from her knee to the dumbbell is 28 cm The weight of her leg is a 33 N with a moment arm horizontal distance of 14 cm from her knee joint i A For this position what torque is created by the dumbbell about her knee joint axis 1 43 82 Nm ii B If the moment arm of the knee extensor muscles is 3 cm about the knee joint axis what amount of force must these muscles produce to hold the leg in the position described 1 F 1460 7 N VII Linear vs Angular Kinetic Analysis a Static Analysis i Systems at rest or constant velocity b Dynamic Analysis i Systems in motion VIII Question 5 a Quentin is lifting a 10 kg dumbbell by pulling upward on it with a 108 1 N force What is the acceleration of the dumbbell as a result of this force i 1 m s2 IX Question 6 a Kristen is spinning on the ice at 50 rad s about her longitudinal axis when she abducts her arms and doubles her radius of gyration about her longitudinal axis from 40 cm to 70 cm If her angular momentum is conserved what is her angular velocity about her longitudinal axis after she increases her radius of gyration i 16 33 rad s X Conservation of Angular Momentum a When gravity is the only external force acting on an object the angular momentum remains constant i This is because the gravitational force acts through the center of mass of an object point of rotation and therefore does not produce a torque b This allows divers and gymnasts to manipulate their angular velocities by changing their moments of inertia XI Question 7 a The average net torque Justin exerts on a discus about its axis of spin is 100 Nm during a throw The mass of the discus is 2 kg and its radius of gyration about the spin axis is 12 cm If the discus is not spinning at the start of Justin s throwing action and the throwing action lasts for 0 20 s how fast is the discus spinning when Justin releases it i 694 44 rad s XII Angular Impulse a Torque applied over a period of time b Impulse change in momentum XIII Question 8 a Tom s leg angularly accelerates 52 36 rad s2 around the hip joint during a roundhouse kick in the transverse plane The moment of inertia of the leg around the axis of rotation for this kick is 0 75 kg m2 How large is the torque that produces this acceleration i 39 27 Nm XIV Question 9 a Doug is driving a gold ball off the tee His downswing takes 0 50 s from the top of the swing until ball impact At the top of the swing the club s angular velocity is zero at the instant of ball impact the club s angular velocity is 30 rad s The swing moment of inertia of the club about the grip is 0 220 kg m 2 What average torque does Doug exert on the golf club during the downswing i 13 2 Nm XV Question 10 a Sarah s twist angular momentum increases from 0 to 50 kg m 2 s in 0 25 s as she initiates a twisting jump on the ice During the 0 25 s her moment of inertia about her twist axis is 2 2 kg …