Small bodies of mass m, and m₂ are attached to opposite ends of a thin rigid rod of length L and mass M. The rod is mounted so that it is free to rotate in a horizontal plane around a vertical axis (see below). What distance d from m, should the rotational axis be so that a minimum amount of work is required to set the rod rotating at an angular velocity ? (Use any variable or symbol stated above as necessary.) + m₂ J MY NOTES m₂
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- A set of reducing gears is used to raise the box as shown below. Pulleys B and C are welded together. B A The diameters of Pulleys A, B and C are 58 cm, 74 cm and 18 cm, respectively. The belt connecting Pulleys A and B has a length of 535 cm. Suppose that Pulley A is rotating at 0.91 revolutions per second. Answer the following, round your answers to at least 3 significant figures and include units. a. How much time does it take the belt to make one revolution if the belt is 535 cm long? b. How much time does it take Pulley B to make one revolution? c. How fast is the box ascending, i.e. what is the vertical speed of the box?The spool shown in (Figure 1) has a mass of 130 kg and a radius of gyration kg = 0.3 m. Figure 250 mm G A -400 mm P Part A If the coefficients of static and kinetic friction at A are μ = 0.2 and = 0.15, respectively, and P = 700 N, determine the angular acceleration of the spool. Express your answer in radians per second squared to three significant figures. VO ΑΣΦ ↓↑ vec a= 13.2 Submit Previous Answers Request Answer X Incorrect; Try Again; 3 attempts remaining Provide Feedback ***** www. ? rad/s² Next >The power of a bus engine is transmitted using the belt-and- pulley arrangement shown. The engine turns pulley A at WA = (30t + 50) rad/s clockwise, where t is in seconds. (Figure 1) Part A Determine the angular velocity of the generator pulley B, measured clockwise, when t = 3 s. Express your answer using three significant figures. Enter positive value if the angular velocity is clockwise and negative value if the angular velocity is counterclockwise. μν ΑΣφ I1 vec WB = rad/s Submit Request Answer Figure Part B Determine the angular velocity of the air-conditioning pulley C, measured clockwise, when t = 3 s. 100 mm Express your answer using three significant figures. Enter positive value if the angular velocity is clockwise and negative value if the angular velocity is counterclockwise. 25 mm WB Πνα ΑΣφ ? vec D. 75 mm wC = rad/s 50 mm WA Submit Request Answer
- A hollow sphere (Icom plane, which is tilted 0 = 18.9 degrees above horizontal. The ball rolls up the incline plane, again without slipping. How far does the ball go up the plane (L) before it comes to a momentary stop? Assume there is negligible loss due to any friction in this process. MR?) of mass 1.25 kg and radius 0.151 m rolls without slipping at a speed of 8.33 m/s toward an inclined Image size: s ML MaxDetermine the angular acceleration of link AB if link CD has the angular velocity wcD = 3 rad/s and angular deceleration aCD = 3 rad/s shown in (Eigure 1). Assume the counterclockwise rotation as positive Figure 1 of 1 Express your answer to three significant figures and include the appropriate units. 0.6 m 0.6 m ? Value O AB rad 0.3 mMember AB has the angular velocity WAB = 4.5 rad/s and angular acceleration a AB = 6 rad/s². (Figure 1) Figure A 200 mm 300 mm @AB a AB B 500 mm 0= 60° 1 of 1 Determine the angular acceleration of member CD at the instant shown measured counterclockwise. Express your answer using three significant figures. Enter positive value if the angular acceleration is counterclockwise and negative value if the angular acceleration is clockwise. aCD = Submit vec Π ΑΣΦ ↓↑ 325 Previous Answers Request Answer X Incorrect; Try Again < Return to Assignment Review Provide Feedback ? rad/s²
- A diver (such as the one shown in the figure(Figure 1)) can reduce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. Figure 1 of 1 Part A If she makes 2.0 rotations in 1.1 s when in the tuck position, what is her angular speed (rev/s) when in the straight position? Express your answer using three significant figures. Submit VE ΑΣΦ Provide Feedback Request Answer ? rev/s Next >Now let's use conservation of energy to calculate the kinetic energy of a rotating cylinder. Specifically, we will employ the work-energy theorem to relate the work done on the cylinder to the change in its rotational kinetic energy. A light, flexible, nonstretching cable is wrapped several times around a winch drum-a solid cylinder with mass 50 kg and diameter 0.14 m that rotates about a stationary horizontal axis turning on frictionless bearings (Figure 1). The free end of the cable is pulled with a constant force of magnitude 9.7 N for a distance of 2.0 m. It unwinds without slipping, turning the cylinder as it does so. If the cylinder is initially at rest, find its final angular velocity w and the final speed v of the cable. Figure F 2.0 m 50 kg 1 of 2 SET UP (Figure 2) shows our sketch for this problem. SOLVE No energy is lost due to friction, so the final kinetic energy K = Iw² of the cylinder is equal to the work W = F's done by the force (of magnitude F, pulling through a…The uniform 22-kg plate is released from rest at the position shown. (Figure 1) Figure A x 0.5 m- 1 of 1 0.5 m > Part A Determine its initial angular acceleration. Express your answer in radians per second squared to three significant figures. Enter positive value if the angular acceleration is clockwise and negative value if the angular acceleration is counterclockwise. a = Submit Part B 195| ΑΣΦ. 41 Request Answer vec ? rad/s² Review Determine the x and y components of reaction at the pin A using scalar notation. Express your answers in newtons to three significant figures separated by a comma.
- thank youSmall bodies of mass m1 and m2 are attached to opposite ends of a thin rigid rod of length L and mass M. The rod is mounted so that it is free to rotate in a horizontal plane around a vertical axis (see below). What distance d from m1 should the rotational axis be so that a minimum amount of work is required to set the rod rotating at an angular velocity ω?Crank AB rotates with a constant angular velocity of 5 rad/s. (Figure 1) Figure 5 rad/s A 600 mm 0 B 300 mm OPPOSED < 1 of 1 150 mm Determine the velocity of block C at the instant 0 = 23°. Assume the direction to the right as positive. Express your answer with the appropriate units. VC = Submit Part B WBC = -- Submit μA Value Request Answer Determine the angular velocity of link BC at the instant 0 = 23 °. Assume the counterclockwise rotation as positive. Express your answer with the appropriate units. μA Value Units Request Answer 2 Units ?