PHY 211 General Physics I CH 10 Worksheet Rotation 1 Rotational Variables 1 Write out the expression for the average angular avg in terms of the angular displacement and elapsed time t 2 Write out the expression for the average angular acceleration avg in terms of the angular velocity and elapsed time t 3 Write an expression for the average angular velocity avg in terms of initial and final angular velocities o and respectively where the angular acceleration is constant 4 Combine your answers to the above exercises and derive the rotational kinematic equations in terms of the angular variables Assume the angular acceleration is constant Rotational Motion 5 An ant is standing on a moving CD 2 cm from the center The CD is moving at 80 rpm a When the CD makes a 45 0o revolution what is the length of the ant s path r b What is the ant s actual linear displacement Dr c What is the rotational speed of the CD expressed in radians per sec d The ant moves to a new position 4 0 cm from the center i What is the angular velocity of the ant compared to its speed at r 2 0 cm ii What is the tangential speed of the ant compared to its speed at r 2 0 cm e The ant then moves to the center of the CD What is the angular velocity and tangential speed of the ant as the CD rotates PHY 211 General Physics I CH 10 Worksheet Rotation 2 Moment of Inertia 6 Calculate the moment of inertia in SI units for the following objects a A 2 kg mass attached to a thin 0 15 m long string a simple pendulum b A 0 5 kg hollow sphere with a 0 10 m diameter Simple Pendulum Hollow Sphere c Two 10 kg solid spheres r 0 05 m attached by a mass less 0 5 m bar simple dumbbell rotated about the middle of the bar Dumbbell d Two 10 kg solid spheres r 0 05 m attached by a mass less 0 5 m bar simple dumbbell rotated about the center of one of the spheres Dumbbell e A meter stick 0 15 kg rotated about its center of mass Meter Stick f A meter stick 0 15 kg rotated about one end Meter Stick Torque 7 Two people are sitting on a 20 kg teeter totter L 7 0 m Person A 60 kg and Person B 30 kg a Person A sits 1 5 m from the fulcrum What is the torque exerted by Person A on the teetertotter assume the mass of the teeter totter itself can be neglected b For the teeter totter to be balanced and in mechanical equilibrium with Person B sitting on the opposing end what torque must Person B apply to the teeter totter Draw a free body diagram of the 2 person teeter totter system c How far from the fulcrum must Person B sit so that the teeter totter balances d Re calculate all of the torques using a fulcrum located at one end of the balanced teetertotter PHY 211 General Physics I CH 10 Worksheet Rotation 3 Kinetic Energy Rotation 8 Determine the rotational kinetic energy for the following objects rotated about the axis described above a A mass attached to a string and rotating at 25 rad sec b A hollow sphere rotating about its center at 15 rad sec c Two 10 kg solid spheres r 0 05 m attached by a massless 0 5 m bar simple dumbbell rotated about the middle of the bar at 15 rad sec d Two 10 kg solid spheres r 0 05 m attached by a massless 0 5 m bar simple dumbbell rotated about the center of one of the spheres at 15 rad sec e A meter stick 0 15 kg rotated about its center of mass at 5 rpm f A meter stick 0 15 kg rotated about one end at 5 rpm 9 Determine the rotational kinetic energy of a 0 15 kg golf ball radius of 2 0 cm a Treat the golf ball as a solid sphere that is rotating at 1000 rpm and simultaneously traveling at 10 m s what is the rotational kinetic energy of the ball b What is the total kinetic energy of the ball PHY 211 General Physics I CH 10 Worksheet Rotation 4 10 Consider 2 attached masses Bugs and Wiley E suspended by a simple solid cylindrical pulley 2 kg Bugs has a mass of 4 kg and Wiley E has a mass of 8 kg The radius of the pulley is 0 1 m Starting from rest Wiley E drops 1 m and Bugs ascends the same amount a Draw a force vector diagram for each object including the pulley Note the tension forces on each end of the rope are not equal 2 kg b Apply Newton s 2nd Law to Wiley E and Bugs Use it to solve for the tension forces T 1 and T2 in terms of g mWiley and mBugs 8 kg c Apply Newton s 2nd Law torque to the pulley 4 kg 1m d Use the expressions for the tension forces in b and the torque equation obtained in c to solve for the acceleration of the system a e What is the magnitude of the tension force at each end of the rope T 1 and T2 respectively f What is KE for Wiley E and Bugs respectively at the end of the 1 m displacement g What is the rotational KE of the pulley at the end of the 1 m displacement h Calculate the total KE and mechanical energy of the system at the end of the 1 m displacement Compare this value with the total KE for the same system where the pulley is mass less
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