Week 12 207

A drum can rotate about a fixed-point O. The A block is attached to a cord wrapping around the drum. The mass of the drum is md = 100kg and the radius is r = 0.5 m. The radius of gyration of the drum about point O is ko=0.3 m. The mass of the block is mb= 20kg. The block is released from rest. The acceleration due to gravity is g=9.81 m/s2.   (1) Calculate the mass moment of inertia of the drum about the point O, IO_______(kgm2) (two decimal places)

A drum can rotate about a fixed-point O. The A block is attached to a cord wrapping around the drum. The mass of the drum is md = 100kg and the radius is r = 0.5 m. The radius of gyration of the drum about point O is ko=0.3 m. The mass of the block is mb= 20kg. The block is released from rest. The acceleration due to gravity g=9.81 m/s2 .   (2) ) If the mass moment of inertia of the drum about point O is IO, and the angular acceleration of the drum is α, select the correct moment equation of the whole drum-block system about the point O._____________       A. mbgr=rmb(rα)   B. 0   C. mbgr=Ioα +rmb(rα)   D. mbgr=Ioα

A disk with mass m = 6.5 kg and radius R = 0.39 m hangs from a rope attached to the ceiling. The disk spins on its axis at a distance r = 1.32 m from the rope and at a frequency f = 18.9 rev/s (with a direction shown by the arrow). what is the torque due to gravity on the disk? what is the period of precession for this gyroscope? what is the direction of precession of the gyroscope?

2 An object is made of two identical uniform 3m long rods connected as shown. The total mass of the system is 60kg. The object can rotate in the plane of the page about a fixed axis at Point A. There is a friction moment of 500 N m about point A. a. What is the mass moment of inertia of the object about Point A? b. If the object is released from rest in the orientation shown, what will be is initial angular acceleration? stationary Mf A = total mass= 60 kg 500 Nm 3 m 3 m g

A constant torque of 2kN-m is exerted on a crankshaft to start the engine.The flywheel has a mass of 1800kg and a radius of gyration 1m .If there is a resisting torque of 1kN-m,find the speed of the engine after 1 minute.

Given: A uniform slender rod is at rest upon a frictionless horizontal surface when a force (F) is applied in the direction shown. Assume that the rod has mass m and length L. A L Horizontal Plane Given that F = 74lb, L = 7.1 ft, mg = 4.6lb, and 0 = 73deg What is the component of acceleration of the mass at point G in the i direction? Answer: Check What is the component of acceleration of the mass at point G in the j direction? Answer: Check What is the component of angular acceleration of the mass in the k direction? (remember your signs) Answer: Check

The wheel shown below has a mass of 5 slugs and a radius of gyration for the z-axis through point Cof 0.7 ft. The spring is massless and has a modulus of 20 lb/ ft and a natural (unstretched) length of 4 ft. Use the acceleration due to gravity, g = 322 ft/sec. The wheel is released from rest, and it rolls without slipping on the plane. Find how far down the plane the mass center Cwill move. Cord wrapped ´around hub IT 1.3 ft 0.8 ftC 3 ft 3 4 0.5 ft

What is the kinetic energy of the following system? Masses m₁ and m₂ are suspended by inextensible strings from the ends of bar B and rotate angles 0₁ and 82, as shown. The bar (length 2) is free to rotate angle a about a horizontal axis, as shown. Its mass moment of inertia about this axis of rotation is I. 772₁ T₁ 771

Find the magnitude and position of the balancing mass at a radius of 13cm by using the analytical method. Three masses m1, m2, m3, are attached to a shaft and revolve in the same plane. The masses are 12kg, 10kg, and 15kg respectively and their radii of rotations are 5cm, 6cm, 7cm respectively. The angular position of the masses m2, m3 are 45° and 145° from the mass m1.

A weight with mass mw=150 g is tied to a piece of thread wrapped around a spool, which is suspended in such a way that it can rotate freely. When the weight is released, it accelerates toward the floor as the thread unwinds. Assume that the spool can be treated as a uniform solid cylinder of radius R=4.00 cm and mass Ms=200 g. Find the magnitude ?a of the acceleration of the weight as it descends. Assume the thread has negligible mass and does not slip or stretch as it unwinds. Use ?=9.81 m/s2.   Find the tension T in the thread.

The 10-kg bar is released from rest in the horizontal position 1 and falls to positions 2. The unstretched lengthy of the spring is 0.6 m and the spring constant is k=20 N/m .what will be the bar 's angular velocity when  it is in position 2.

A spinning top consists of a ring (which can be treated as a cylindrical shell) of mass m = 0.52 kg and a radius of 60 mm is mounted on its central pointed shaft with spokes. The spokes and pointed shaft have negligible mass meaning that their inertia can be neglected. The top has a spin velocity of 10,000 rev/min and is released on a horizontal surface with the point at O remaining at a fixed point. Assuming that the spin angular velocity is high when compared to the precession, determine the magnitude of the precession angular velocity of the top. 15° 60 mm 80 mm 10000 rev/min O 1.2 rad/sec 0.6 rad/sec 0.2 rad/sec 2.1 rad/sec

A spinning top consists of a ring (which can be treated as a cylindrical shell) of mass m = 0.52 kg and a radius of 60 mm is mounted on its central pointed shaft with spokes. The spokes and pointed shaft have negligible mass meaning that their inertia can be neglected. The top has a spin velocity of 10,000 rev/min and is released on a horizontal surface with the point at O remaining at a fixed point. Assuming that the spin angular velocity is high when compared to the precession, determine the magnitude of the precession angular velocity of the top. 15° 60 mm 80 mm 10000 rev/min

The 2-mass system shown below depicts a disk which rotates about its center and has rotational moment of inertia Jo and radius r. The angular displacement of the disk is given by 0. The spring with constant k₂ is attached to the disk at a distance from the center. The mass m has linear displacement & and is subject to an external force u. When the system is at equilibrium, the spring forces due to k₁ and k₂ are zero. Neglect gravity and aerodynamic drag in this problem. You may assume the small angle approximation which implies (i) that the springs and dampers remain in their horizontal / vertical configurations and (ii) that the linear displacement d of a point on the edge of the disk can be approximated by d≈re. Ө K2 www m 4 Cz 777777 Jo Make the following assumptions when analyzing the forces and torques: тв 2 0>0, 0>0, x> > 0, >0 Derive the differential equations of motion for this dynamic system. Start by sketching LARGE and carefully drawn free-body-diagrams for the disk and the…

A relatively thin disc with uniformly distributed mass is mounted on a shaft which rotates at 1000 RPM. To conduct a test, two extra masses are added to the disc at the positions shown in Figure Q10. Masses A and B introduce known unbalances of 2 kgmm and 4 kgmm, respectively. Determine the angular location of the correction mass measured from y-axis in the clockwise direction and the centrifugal force that it needs to produce in order to balance the system. YA A 30° B 70° X TIT TIT N

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A motorcycle and rider have a combined mass of 350kg. At another point in its journey, the motorcycle and rider travel at 80 km/h around a left-hand bend of radius 30m. Calculate:     The angular velocity of each wheel, the moment of inertia of each wheel. The angular momentum of the wheel prior to entering the bend. and the magnitude of the gyroscopic torque produced on the bike as the rider is driving around the bend.       What is the effect and why is it important to calculate the gyroscopic torque produced on the bike as the rider is driving around the bend? How can you enhance this system?

The arms of a Porter governor are each 250 mm long and pivoted on the governor axis. The mass of each ball is 5 kg and the mass of the central sleeve is 30 kg. The radius of rotation of the balls is 150 mm when the sleeve begins to rise and reaches to certain radius at maximum speed. The governor has radius that is 175 mm at mid position. The speed range of the governor is 38 rpm, and the increment in speeds is constant in the three positions. Find : (1) the friction of the load which existed at the sleeve, and (2) the governor radius at maximum speed. The friction is ignore in mid position only.

A top consists of a spinning disc of radius 50 mm and mass 0.8 kg mounted at the end of a light rod as shown. If the disc rests on a pivot with its axis of spin horizontal as shown, and the distance X is 30 mm. calculate the velocity of the precession when its spins at 40 rev/min.

The accelerating torque increases the speed of a flywheel from x rpm to y rpm in 15 seconds. Find 1. The accelerating torque produced during the above period. 2. Increase in the kinetic energy of the flywheel 3. Change in the angular momentum of the flywheel. 4. Number of revolutions made by the flywheel during this period. 5. Find the braking torque required to stop the flywheel completely. Assume suitable mass and radius of gyration. Also assume suitable values for rpm x and y above.