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- + G In the above diagram, the wheel starts from rest and rolls without slipping. The force (you don't need the value) causes a constant angular acceleration of 7.112 rad/s2. The radius of the wheel is R - 0.392 m. What is the magnitude of the acceleration of the point at the top of the wheel at time t 1.400 s? This is the point at the outer edge directly above the center of gravity, Gwhere the force F connects to the wheel. Use units of m/s. Don't place units in your answer, 3 oAn electric motor has a rotor with a mass moment of inertia of 22 ft-lb-s2. What torque is required to accelerate it from rest to 1,174 rpm in 3.6 seconds? Provide your answer in lb-ft and round to the nearest whole number. An electric motor has a rotor with a mass moment of inertia of 22 ft-lb-s2. What torque is required to accelerate it from rest to 1,174 rpm in 3.6 seconds? Provide your answer in lb-ft and round to the nearest whole number.The dimensions of the various links of a mechanism, as shown in Fig. 3, are as follows: OA = 0.3 m: AB = 1 m: CD = 0.8 m; and AC = CB. If the crank OA rotates at 100 rpm. in the anticlockwise direction, find, for the given configuration: 1. velocity and acceleration of B and D: 2. angular acceleration of the links AB and CD. 45 0.6 m- Eig 3
- Q1. Member AB is rotating (about fixed point A) with angular velocity (@ = 1 rad/sec) and angular acceleration (a = 2 rad/sec?) and driving the link CD (rotating about fixed point D at constant velocity) as shown in figure. Select five right answers. (a) Tangential Acceleration (a:) of link AB will not be zero (b) Tangential Acceleration (a) of link AB will be zero D 450mm (c) Tangential Acceleration (a,) of link CD will not be zero 200 mm 100 mm 60 H (d) Tangential Acceleration (a,) of link CD will be zero (e) All points on link CB will have same linear velocity 0 All points on link CB will have same angular velocity Formula • Tangential acceleration of a rotating link -ra • Radial (normal) acceleration of a rotating link = v³ /r= wr velocity of a rotating Ink (v) = r.w (g) Angular acceleration (a) for link CD will be zero (h) Angular acceleration (a) for link CB will not be zero Q2. Magnitude of linear velocity of any point “H" located at the half of the length of a rotating link CB…The following diagram shows a piston moving in a cylinder with rod AB. Point B is rotating clockwise with an angular velocity of w. cylinder piston A connecting rod crank bearing B ResearchGate The motion of B is given by the equation r = C cos(wt) + Dsin(wt) Were r is the horizontal +vertical distance of B from O, and C, D are constants. For C=D=42mm and w = 20 rad/s. (i) Write r in the form Rcos (wt ± ß) and state the amplitude and period of r. (ii) Sketch one complete cycle of r. (iii) Explore the differences between the derived form and drawn formA particular bicycle has wheels that are 66 cm in diameter. The radius of the crank armis 18 cm. At its lowest point, the pedal is 16 cm above the ground. A person is pedalingthe bicycle such that the crank arm rotates once every second.Questions:1. Write an equation that models the vertical position of the foot with respect to theground, starting from the lowest point, as the crank arm turns.2. What is the rate of change of the vertical position of the foot when it is at themidline? Explain your answer3. How fast, in kilometres per hour, is the bicycle moving?4. Determine an equation that would model the foot’s position when the cyclist istraveling 5 km/h. Compare this equation to your equation from question 1 andexplain any differences.5. Use calculus to explain why the rotation velocity of a point on the perimeter of awheel is the same as the velocity of the pedal. Use examples to support youranswer.
- The below figure shows a cylinder of 13 kg mass, 0,3 m radius, undergoing unconstrained planar motion under the action of two forces F1=181 N and F2=76 N as shown. Calculate the angular acceleration of the cylinder in rad/s2. (Hint: I=½mr2) (If the direction of the angular acceleration is CCW, just enter the value of it without any sign. If it has CW direction, enter "-" sign "negative sign" before the value such as "- 12,12". Allowable tolerance for this question is relatively 2 percent.) F2 FiThe iillustration depicts a prototype design for the High-G Rover. It is made up of an arm that is attached to a shaft that is pinned to a disk. The aarm has a retractable shaft that extends and contracts to cause the disk to rotate. To make the computation easier, let us assumee that the arm does nott rotate A. If the arm's total length is L = 640mm, the distance from the centre of the disk to the shaft pin is r = 112mm, and the arm rotates clockwise at a constant angular velocity of 250.273 rpm. 1.) Would an increase in angular velocity increase point C's linear velocity relative to point A? If so, why or why not? a.) What is the linear velocity of point C with respect to point A if the angular position of the pin (between AB and BC) is 0.578 radians? b.) What is the distance between points A and C if the angular position of the pin (between AB and BC) is 0.578 radians? c.) What is the linear velocity of point C with respect to point A if the angular velocity is increased by 34.34…A load is raised 11 ft by the gears and wheel system below. Gear A is initially rotating at rest and accelerates uniformly to omega = 24 rpm in t= 10 sec and maintain then maintain this constant 24 rpm speed. The dimensions are rA= 1 in, rB= 9 in and rC=16 in. 2) After 10 sec, find the distance s2 in feet and in NC es needed to reach the 11 ft, find thetaC2(t), alphaA2, alphaB2 in rad/s^2, omegaA2(t), omegaB2(t) in rad/s, thetaA2(t), in rad and the distance s2 in ft that should be made to get to the 11 ft raising distance of the load. 3) Deduce the number of revolutions made by gear A and how long it will take, to raise the load up to 11 ft.
- A shaft is rotating at a uniform speed with four masses m1, m2, m3 and m4 of magnitudes 300 kg, 450kg, 360kg and 390 kg respectively. The masses are rotating in the same plane. The corresponding radii of rotation are 200mm, 150mm, 250mm and 300mm. The angles made by these masses with respect to horizontal are 0°, 45°, 120° and 255° respectively. 1) Check the magnitude and position of balance mass if it radius of rotation is 200mm, and 2) Evaluate the effect of adding the balance mass to the system. solve it using garphical methodIn a manufacturing process, a large, cylindrical roller is used to flatten material fed beneath it. The diameter of the roller is 7.00 m, and, while being driven into rotation around a fixed axis, its angular position is expressed as 0 = 2.10t? - 0.800r where 0 is in radians and t is in seconds. (a) Find the maximum angular speed of the roller. rad/s (b) What is the maximum tangential speed of a point on the rim of the roller? m/s (c) At what time t should the driving force be removed from the roller so that the roller does not reverse its direction of rotation? |s (d) Through how many rotations has the roller turned between t = 0 and the time found in part (c)? | rotationsPROBLEM 2 For the mechanism, shown on the figure, Onc = const 5 s'. O4=BC D0,3 m, AB-0,6 m. Determine: a) velocity and acceleration of the point B: b) angular acceleration of the body BC: c) angular velocity and angular acceleration of the body OA: d) linear velocity and acceleration of the pointA. 120 60°