a)
with given values:
b)
c)
Torque on the flywheel:
rotational equation of motion:
Equation of motion for the 30 kg mass
we already found acceleration
From the figure:
differentiating it twice
Now consider:
d)
vertical reaction is given by:
3. An experiment is set up as shown in Figure Q3 to measure the moment of...
The pulley shown (Figure 1) has a moment of inertia IA = 0.625 kg⋅m2 , a radius r = 0.250 m , and a mass of 20.0 kg. A cylinder is attached to a cord that is wrapped around the pulley. Neglecting bearing friction and the cord’s mass, express the pulley’s final angular velocity in terms of the magnitude of the cord’s tension, T (measured in N), 4.00 s after the system is released from rest. Use the principle of...
an 8kg flywheel of radius r is initially at rest. assume the radius of the gyration kG= 0.12m and the radius of the flywheel r = 0.125m. an object B also of mass 8 kg is attached to a cord that is wrapped around a periphery of the flywheel. the fly wheel starts to rotate clockwise with angular velocity. the rotation is resisted by a constant frictional torque mf in the bearing 1Nm. use the work energy principle to determine...
Hi, can you solve the question for me step by step, I will rate up if the working is correct. I will post the answer together with the question. Answer: Question 7 Implement the following: A reel consists of two solid uniform circular discs, each of mass m and radius 2R, attached to two ends of a solid uniform cylindrical axle of mass m and radius R. The reel stands on a rough horizontal table. A light inextensible string has...
One simple way to measure the moment of inertia of an irregular object is shown in the diagram. The object is mounted on a frictionless axis. A light string is wrapped around the object, passes over a light pulley (so it has negligible moment of inertia itself), and then connected to mass M = 40.6 kg. The system is released from rest. After mass M has fallen distance 4.05 m it is moving 2.67 m/s and the object has reached...
1) The parallel axis theorem provides a useful way to calculate the moment of inertia I about an arbitrary axis. The theorem states that I = Icm + Mh2, where Icm is the moment of inertia of the object relative to an axis that passes through the center of mass and is parallel to the axis of interest, M is the total mass of the object, and h is the perpendicular distance between the two axes. Use this theorem and...
59 The figure shows a tabletop experiment that can be used to determine an unknown moment of inertia. A rotating platform of radius R has a string wrapped around it. The string is threaded over a pulley and down to a hanging weight of mass m. The mass is released from rest, and its downward acceleration a (a > 0) is measured. Find the total moment of inertia I of the platform plus the object sitting on top of it....
please solve it as soon as possible and be sure of your answers A cylinder of mass m and mass moment of inertia J is free to roll without slipping but is restrained by 3 springs of stiffinesses k. If the translational and angular displacements of the cylinder are x and 8 from its equilibrium position. Determine the following: a- Equation o method b- Find the natural frequency of vibration f motion of the system assuming that the system is...
Q3 - Determine the moment of inertia of the aluminum ring, Iring, shown in Figure 3 given the following parameters associated with the ring: mass M = 61 grams; and inner and outer radii, a = 6.35 cm and b = 7.6 cm, respectively. Q4 - A 108 gram Frisbee is 24 cm in diameter and has about half its mass spread uniformly in a disk, while the other half is concentrated in the rim of the Frisbee. With a...
3. In the figure above, a spool or pulley with moment of inertia MR2 is hanging from a ceiling by a (massless, unstretchable) string that is wrapped around it at a radius R, while a block of equal mass M is hung on a second string that is wrapped around it at a radius r as shown. Find the magnitude of the acceleration of the the central pulley.
0.27 m0.24 m0.06 m Q3. The assembly in the figure is composed of three homogeneous bodies: the 10-kg cylinder, the 2-kg slender rod and the 4-kg sphere. For this assembly, calculate (a) , the mass moment of inertia about the x-axis and (b) I, and k, the mass moment of inertia and the radius of gyration about the central axis of the assembly. 0.15 m 0.09 m 2 kg 0.15 m 4 kg 10 kg