A hollow cylinder of mass M1 and radius R1 rolls without slipping on the inside surface of another hollow cylinder of mass M2 and radius R2. Assume R1<
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- A uniform solid disk with radius 11 cm has mass 0.5 kg (moment of inertia I = ½MR2). A constant force 12 N is applied as shown. At the instant shown, the angular velocity of the disk is 40 radians/s in the −z direction (where +x is to the right, +y is up, and +z is out of the page, toward you). The length of the string d is 14 cm. After the torque has been applied for 0.2 s, what are the magnitude and direction of the angular momentum about the center of the disk? At this later time, what are the magnitude and direction of the angular velocity of the disk?I am working on this problem and I think I am pretty close but I keep getting wrong answers. How do I do this? In this problem, I am solving for h.3
- A uniform hoop of mass m and radius R rolls down an inclined plane of length I without slipping. The plane, which is originally horizontal, is lifted up at a constant rate such that the angle of the plane with the horizontal at time t is o = wt (see figure). R g O = 0 t (a) i. q and 0 are not independent. If 0 = 0 when q = 1, determine the relation between them. ii. Determine the height of the centre of mass of the hoop above the base of the plane. iii. Hence show that the Lagrangian of the body, expressed in terms of the distance q from the pivotal point of the plane, is L = ma² +ms'q? – mg(a sin wt + Rcos wt). (b) Determine the Euler-Lagrange equations for the system. Note: you may assume the Lagrangian equations of motion for generalised co-ordinates q:: d (OLA hoop, a disk, and a solid sphere with equal masses and equal radii, all roll without slipping down an inclined plane starting from rest. Which of the following is NOT true? (Inoop = mr? ; Idisk = mp ; Isolid sphere = mr2) O The force of gravity along the plane will be equal for all. O At the bottom, the rotational kinetic energy will be greatest for the sphere. O At the bottom, the angular velocity about the center of the object will be greatest for the sphere. O At the bottom, the rotational plus translational kinetic energy will be the same for each object. O At the bottom, the translational kinetic energy will be least for the hoop.The rotation of a 11 kg motorcycle wheel is depicted in the figure. The wheel should be approximated to be an annulus of uniform density with inner radius R1 = 27 cm and outer radius R2 = 33cm. Randomized Variables ω = 132 rad/sR1 = 27 cmR2 = 33 cm m = 11 kg Calculate the rotational kinetic energy in the motorcycle wheel if its angular velocity is 132 rad/s in J.
- Consider the force vector F=<1,1,1/2>. If the magnitude of the torque T=OP*F is equal to the area of the equilateral triangle formed by the origin, P, and (1,-1,1), then determine the acute angle formed by OP and F. Give your answer in degrees.In a popular game show, contestants give the wheel a spin and try to win money and prizes! The wheel is given a rotational velocity and this rotation slows down over time and the wheel eventually stops. One contestant gives the wheel an initial angular velocity (ωi).. Because of friction, the wheel eventually comes to rest (ωf = 0 radians/sec) in time t. c.)What is the Δθ of the wheel as it comes to a stop?The bent flat bar rotates about a fixed axis through point O. The angle can be found at any instant according to this relation 8 = π * sin(t), where 9 is in rad and it is in seconds. At this instant, determine the instantaneous velocity and acceleration of point A. Note: w=0, a = ö. Also, you must change the angle from (Degree) to (Rad) α T 0.5 m, A 0.3 m 105⁰ 30°
- A particle of mass m in the figure below slides down a frictionless surface through height h and collides with a uniform vertical rod (of mass M and length d), sticking to it. The rod pivots about point O through an angle θ when it momentarily stops. Find θ in terms of m, M, g, h, d and various constants. (Please type answer no write by hend)A circular disc of mass M and radius R is rotating about its axis with angular speed ω1 . If another stationary disc having radius R/2 and same mass M is droped co-axially on to the rotating disc. Gradually both discs attain constant angular speed ω2. The energy lost in the process is p% of the initial energy. Value of p isA hollow ball of mass m = 2.0 kg and radius r rolls without slipping along a loop-the-loop track, with a height of h and radius R. The ball is released from rest somewhere on the straight section of the track. a. From what minimum height h above the bottom of the track must the ball be released in order that it not leave the track at the top of the loop? (height of loop is 2R) The Radius is 10.0 m b. What is acting as a radial force at the top of the loop? (gravity, Tension ???) I hollow ball = (2/3) mr² gninub 21 noitu boxil bns brossz sri gnitub suprot sit zomit auol (C doum asmuomo (3 2R di grois un 12 What was the potential energy at the top of mass m? Houm