7 A horizontal circular disk of uniform thickness radius a

Last updated: 6/10/2023

7 A horizontal circular disk of uniform thickness radius a and weight I can rotate freely about its vertical geometric axis Fig F Along a circular track of radius r a particle of weight Q is travelling Initially the disk and the particle are rest what angular velocity will the disk acquire if the particle begins to travel along the track with a constant speed v relative to the disk Assume W 10 lb Q 1 lb a 10 in r 6 in v 4 fps Ans 0 537 sec 8 Owing to cooling the linear dimensions of a solid homogeneous sphere uniformly rotating about a diameter diminish by 0 1 per cent What effect will this have on the angular velocity of there is no external moment with respect to the diameter of the sphere Ans The angular velocity increases by 0 2 percent 9 The wheel of a small gyroscope is set spinning by pulling on a string wound around the shaft The moment of inertia of the wheel is 0 045 Ib sec in and the diameter of the shaft on which the string is wound is 1 2 in If 36 in of string is pulled off with a constant force of 12 lb what rpm will be imparted to the wheel An 1 324 rpm at 10 A slender prismatic bar of total length 21 and weight 2W is bent in a right angle its middle point 0 and hangs from a hinge at this point as shown in Fig G Find the maximum angular velocity 8 that the bar will acquire if released from rest in the position shown Ans 0 0 621g l 11 If the slender prismatic bar AB shown in Fig H is released from rest in the horizontal position and rotates about A under the influence of gravity find the reaction at A as it swings through the vertical positions Ans R 5W 2 NG F volls FG G FIG 11 12 A slender prismatic bar DE of length I and weight is rigidly attached at its mid point C to a shaft AB and makers therewith an angle a as shown in Fig L Determine the kinetic energy T of the bar of it rotates with constant angular velocity about AB The following numerical data are given W 20 lb 1 40 in a 45 and the uniform angular speed is 200 rpm Ans T 755 in lb 13 A homogeneous slender prismatic bar AB of length and weight Wis hinged at its lower end 4 and can rotate freely in the vertical plane as shown in Fig If the bar is released from rest in the unstable position and falls over under the influence of gravity calculate the horizontal component of the reaction at A when 30 Ans X 0 225 W K mwin 15 In Fig K a rotor of weight W 386 lb and radius of gyration ie 4 in is mounted on a horizontal shaft and set in rotation by a falling weight W 386 lb as shown If the system is released from rest find the velocity of the block after it has fallen through a distance of 10 ft Ans v 11 35 fps HG 1 14 What initial angular velocity a should be given to the bar AB in Fig J in the top position in order that it will swing through the lowest position B vertically below A with angular velocity 2m Ans 2g l 16 A homogeneous plate 1 ft square is supported in a vertical plane as shown in Fig L a If the pin at 8 is removed what angular velocity u will the plate acquire by the time the diagonal AC becomes vertical b Calculate vertical reaction Re for the instant when the diagonal AC of the square is vertical Ans a e 4 47 rad sec b R 1 44 10 J LA