Physics C Rotational Motion Name: AP Review Packet

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Physics CRotational MotionAP Review PacketLinear and angular analogsLinearRotationx position x displacementv velocityaT tangential accelerationVectors in rotational motionUse the right hand rule to determine direction of thevector!Don’t forget centripetal acceleration!aR ac v2/rKinematic equations for angular and linear motion.Kinematic Equations 1v vo at o tKinematic Equations 2x xo vot 1/2at2 o ot 1/2 t2Kinematic Equations 3v2 vo2 2a(x xo) 2 o2 2 ( o)Rotational InertiaRotational analog of massFor point massesI mr2I: rotational inertia (kg m2)m: mass (kg)r: radius of rotation (m)For solid objectsI r2 dmParallel Axis TheoremI Icm M h2I: rotational inertia about center of massM: massh: distance between axis in question and axisthrough center of massKinetic EnergyKtrans ½ M vcm2Krot ½ I 2Kcombined ½ M vcm2 ½ I 2Rolling without slipping uses both kindsK ½ M vcm2 ½ I 2v rK ½ M vcm2 ½ Icm vcm2/R2orK ½ M 2R2 ½ Icm 2Name:TorqueTorque is the rotational analog of force.A “twist” (whereas force is a push or pull).Torque is a vector) r F r F sin R: moment arm lengthF: force : angle between moment arm and point ofapplication of force. I (think F ma) : torqueI: rotational inertia : angular accelerationWork in rotating systemsWrot (think W F d)Wrot : work done in rotation : torque : angular displacementPower in rotating systemsProt (think P F v)Prot : power expended : torque : angular velocityStatic Equilibrium 0 F 0Angular momentumFor a particleL r pFor a system of particlesL LiFor a rigid bodyL I (think P mv)Conservation of Angular MomentumAngular momentum of a system will not changeunless an external torque is applied to the system.LB LAI B I A(one body) lb la(system of particles)Angular momentum and torque dL/dt (think F dP/dt) : torqueL: angular momentumt: timeTorque increases angular momentum when parallel.Torque decreases angular momentum when antiparallel.Torque changes the direction of the angular momentumvector in all other situations.PrecessionThe rotating motion made by a spinning top or gyroscope.Precession is caused by the interaction of torque andangular momentum vectors. dL / dt r F

Physics CRotational MotionAP Review PacketMULTIPLE CHOICEPRACTICE PROBLEMS1. A wheel spinning at 3 m/s uniformlyaccelerates to 6 m/s in 4 s. Its radius is 20 cm.How far around the wheel will a speck of dusttravel during that interval?A) 6 mD) 18 mB) 9 mE) 30 mC) 12 m2. If an object of radius 3 m thatexperiences a constant angular accelerationstarting from rest, rotates 10 rads in 2 s, whatis its angular acceleration?A) 2.5 rad/s2D) 10 rad/s22B) 5 rad/sE) 15 rad/s22C) 7.5 rad/sName:Base your answers to questions 4 and 5 on thefollowing situation.An object weighing 10 N swings at the end of arope that is 0.72 m long as a simple pendulum. Atthe bottom of the of the swing, the tension in thestring is 12 N.4. What is the magnitude of thecentripetal acceleration at the bottom of theswing?A) 2 m/s2D) 12 m/s2B) 4 m/s2E) 22 m/sC) 10 m/s25. What is the speed of the object at thebottom of the swing?A) 0.6 m/sD) 2.4 m/sB) 1.2 m/sE) 7.2 m/sC) 2.0 m/sBase your answers to questions 6 and 7 on thepicture below, which represents a rigid uniformrod with a mass of 6kg and a length of 1.0 m ispivoted on the right end. It is held in equilibriumby an upward force of 40 N.3. A bicycle moves at constant speedover a hill along a smoothly curved surface asshown above. Which of the following bestdescribes the directions of the velocity and theacceleration at the instant it is at the highestposition?A) The velocity is towards the right of the pageand the acceleration is towards the top of thepage.B) The velocity is towards the right of the pageand the acceleration is towards the bottom ofthe page.C) The velocity is towards the right of the pageand the acceleration is towards the bottomright of the page.D) The velocity is towards the right of the pageand the acceleration is towards the top rightof the page.E) The velocity is towards the top right of thepage and the acceleration is towards thebottom right of the page.6. How far from the left end of the rodshould the force be placed to maintainequilibrium?A) 10 cmD) 40 cmB) 20 cmE) 50 cmC) 25 cm7. What force is applied to the rod bythe pivot?A) 10 ND) 60 NB) 20 NE) 100 NC) 40 N

Physics CRotational MotionAP Review Packet8. A uniform wooden board of mass 10M is held up by a nail hammered into a wall. Ablock of mass M rests L/2 away from the pivot.Another block of a certain mass is hung adistance L/3. The system is in staticequilibrium.Name:12. What is the moment of inertia of aspinning object of radius 0.5 m and mass 6 kgmoving at 5 m/s, if it has a kinetic energy of 100 J?A) 1 kg m2D) 8 k gm22B) 2 kg mE) 20 kg m22C) 4 kg m13. Which of the following objects has theleast kinetic energy at the bottom of the incline ifthey all have the same mass and radius?A) cylinderD) all have the sameB) sphereE) not enough informationC) hoopWhat is the measure of the mass labeled "?" ?A) MD) 3M22B) ME) 2M3C) M29. The angular velocity of a rotatingdisk with a radius of 2 m decreases from 6 radsper second to 3 rads per second in 2 seconds.What is the linear acceleration of a point onthe edge of the disk during this time interval?A) ZeroD) 3/2 m/s22B) –3 m/sE) 3 m/s2C) –3/2 m/s210. A solid sphere of radius 0.2 m andmass 2 kg is at rest at a height 7 m at the top ofan inclined plane making an angle 60 with thehorizontal. Assuming no slipping, what is thespeed of the cylinder at the bottom of theincline?A) ZeroD) 6 m/sB) 2 m/sE) 10 m/sC) 4 m/s11. A spinning object with moment ofinertia I increases in angular speed from 0to a in t seconds. What is the average powerdelivered to the object during this interval t?A) I a/2t2B) I a2/tC) I a2/2tD) I a2/t2E) I a2/2t214. Which of the following objects has thegreatest rotational kinetic energy at the bottom ofthe incline if they all have the same mass & radius?A) cylinderD) all have the sameB) sphereE) not enough informationC) hoop15. A solid cylinder of radius .2 m and mass2 kg is at rest at a height 1.2 m at the top of aninclined plane making an angle 60 with thehorizontal. Assuming no slipping, what is thespeed of the cylinder at the bottom of the incline?A) ZeroD) 6 m/sB) 2 m/sE) 10 m/sC) 4 m/s16. What is the ratio of the moment ofinertia of a cylinder of mass m and radius r tothe moment of inertia of a hoop of the samemass and same radius?A) 1:1D) 1:4B) 1:2E) 4:1C) 2:117. A 4 kg object moves in a circle ofradius 8 m at a constant speed of 2 m/s. Whatis the angular momentum of the object withrespect to an axis perpendicular to the circleand through its center?A) 2 N sD) 24 m2/sB) 6 N m/kgE) 64 kg m2/sC) 12 kg m/s18. A solid cylinder with diameter 20 cmhas an angular velocity of 10 m/s and angularmomentum of 2 kg m2/s. What is its mass?A) 0.1 kgD) 5 kgB) 1 kgE) 10 kgC) 2 kg

Physics CRotational MotionAP Review PacketFREE RESPONSE 1Name:

Physics CRotational MotionAP Review PacketFREE RESPONSE 2Name:

Physics CRotational MotionAP Review PacketFREE RESPONSE 3Name:

Physics C Rotational Motion Name:_ AP Review Packet 8. _A uniform wooden board of mass 10 M is held up by a nail hammered into a wall.A block of mass M rests L/2 away from the pivot. Another block of a certain mass is hung a

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