Trot-1 A small wheel and a large wheel are connected by a belt. The small wheel is turned at a constant angular velocity s. How does the magnitude of the angular velocity of the large wheel L compare to that of the small wheel?A) s = LB) s > LC) s < LThere is a bug S on the rim of the small wheel and another bug L on the rim of the large wheel. How do their speeds compare?A) S = L B) S > L C) S < LAnswers: s > L Every time the big wheel turns once, the little wheel turns several times. So the small wheel turns thru more radians per sec. S=L. Because the wheels are connected by a belt which does not slip, when one bug moves an inch along the rim, so does the other bug. Trot-2 A pocket watch and Big Ben are both keepingperfect time. Which minute hand has the largerangular velocity ?A) Pocket watch's B) Big Ben's C) Same onboth.sLpocket watch Big BenAnswer: Both Big Ben and the pocket watch have the same magnitude angular velocityTrot-3 A ladybug is clinging to the rim of a spinning wheel which is spinning CCW very fast and is slowing down. At the moment shown, what is the approximate direction of theladybug's acceleration?A) B)  C) D) E) Answer: The direction of the acceleration a is the same as the direction of v. The v1-v2-v diagram looks like:Trot-4 A student in Physics 2010 sees the following question 1 on CAPA due the following Friday night.An engine flywheel turns with constant angular speed of 100 rev/min. When the engine isshut off, friction slows the wheel to rest in 2 hours. What is the magnitude of the constant angular acceleration of the wheel? Give the answer in units of rev/min2.The student writes 0 02 f 2 (100 rev/min), so t t t 120 minw- w wp pa = a = = =Does the answer come out correctly with the desired units?A) Yes B) NoAnswer: No! You would write the exactly the same equations above if you were trying to get the answer in rad/min2. The factor of 2 in the equation is actually 2 rad/rev, so the units of the answer above are really rad/min2. If you want the answer in rev/min2, you v1v2vv1v2have to leave out the factor of 2 , or you can convert the answer in rad/min2 to rev/min2 by multiplying by the conversion factor (1 rev/2 rad). CTRot-5 Three forces labeled A, B, C are applied to a rod which pivots on an axis thru its center. [0 0cos(45 ) sin(45 ) 1/ 2 0.707= = =].Which force causes the largest magnitude torque? A B C D) two or more forces tie for largest size torque.Answer: A. For C, . For B, . For A, . CTRot-6 A mass is hanging from the end of a horizontal bar which pivots about an axis through it center, but it being held stationary. The bar is released and begins to rotate. Asthe bar rotates from horizontal to vertical, the magnitude of the torque on the bar..A) increases B) decreases C) remains constant2F F F 45o L/4 L/2 L A C BAs the bar rotates from horizontal to vertical, the magnitude of the angular acceleration  of the bar..A) increases B) decreases C) remains constantAnswers: The torque decreases! F decreases as the mass falls. When the bar is vertical, F and the torque is zero. As the bar rotates, the angular acceleration decreases. . Here I, the moment of inertia, is constant. The torque  decreases (problem above), so the angular acceleration must decrease. CTRot-7 A mallet consists of a heavy steel cubical head on a light wooden handle. About which axis of rotation is the moment of inertia I a maximum?Answer: Axis B. This axis is farthest from the massive hammer head, so for this axis the moment of inertia will have the largest ri's . CTRot-8 Consider a rod of uniform density with an axis of rotation through its center and an identical rod with the axis of rotation through one end. Which has the larger moment of inertia?ABCDA) IC > IEB ) IC < IEC ) IC = IEAnswer: IE > IC If more of the mass is further from the axis, then the moment of inertia is bigger.CTRot-9 Consider two masses, each of size 2m at the ends of a light rod of length L withthe axis of rotation through the center of the rod. The rod is doubled in length and the masses are halved. What happens to I?A) IA > IBB ) IB > IAC) IA = IBAnswer: IA < IB axisaxisC EAB2m2mL/2L/2mLLmCTRot-10 A mass m hangs from string wrapped around a pulley of radius R. The pulleyhas a moment of inertia I and its pivot is frictionless. Because of gravity the mass falls and the pulley rotates.The magnitude of the torque on the pulley is..A) greater than mgRB) less than mgRC) equal to mgR(Hint: Is the tension in the string = mg?) Answer: The magnitude of the torque is less than mgR! The tension in the string is less than mg because the mass is accelerating down. Considering the motion of the mass m, we get The tension in the string FT is less than mg. The torque is RFT which is less than Rmg. CTRot-11 Consider a solid disk with an axis of rotation through the center (perpendicular to the diagram). The disk has mass M and radius R A small mass m is placed on the rim of the disk. What is the moment of inertia of this system?A) (M+m)R2B) less than (M+m)R2C) greater than (M+m)R2RmmMRAnswer: less than (M+m)R2 Itotal = IDisk + Im = (1/2)MR2 + mR2 = [(1/2)M + m]R2 CTRot-12 Two light (massless) rods, labeled A and B, each are connected to the ceiling by a frictionless pivot. Rod A has length L and has a mass m at the end of the rod. Rod Bhas length L/2 and has a mass 2m at its end. Both rods are released from rest in a horizontal position. Which one experiences the larger torque?A) A B) B C) Both have the same size .Which one has the largest moment of inertia I (about the pivot)?A) A B) B C) Both have the same size IWhich one falls to the vertical position fastest?A) A B) B C) Both fall at the same rate.(Hint: I)Answers: Both have the same size torque.  A = RFsin = Lmg sin.  B = RFsin = (L/2)2mg sin= Lmg sin The one with the smallest I has the largest  (since both have the same torque). IA = mL2, IB = 2m (L/2)2 = (1/2) mL2. IB has a smaller I, a larger  , so it falls faster. L L/2 m 2m A BCTRot-13 Two hoops, A and B, both with the same mass M , are each rotating about an axis thru the center. Hoop B has twice the diameter and is rotating at twice the rate (twice the ) as hoop A. What is the ration KEB / KEA ?A) 2 B) 4 C) 6 D) …