- The pipe has a mass M and is held in place on the truck bed using the two boards A and B. Determine the acceleration of the truck so that the pipe begins to lose contact at A and the bed of the truck
- The drop gate at the end of the trailer has mass M and mass center at G. If it is supported by the cable AB and hinge at C, determine the tension in the cable when the truck begins to accelerate at
- The sports car has mass M and a center of mass at G. Determine the shortest time it takes for it to reach speed v, starting from rest, if the engine only drives the rear wheels, whereas the front
- Angular motion is transmitted from a driver wheel A to the driven wheel B by friction between the wheels at C. If A always rotates at constant rate ωA and the coefficient of kinetic friction between
- The conical spool rolls on the plane without slipping. If the axle has an angular velocity ω1 and an angular acceleration α1 at the instant shown, determine the angular velocity and angular
- Gear A is fixed while gear B is free to rotate on the shaft S. If the shaft is turning about the z axis with angular velocity ωz, while increasing at rate αz, determine the velocity and
- If the hoop has a weight W and radius r and is thrown onto a rough surface with a velocity vG parallel to the surface, determine the amount of backspin, ω0, it must be given so that it stops
- If the collar at A is moving downward with an acceleration aA, at the instant its speed is vA, determine the acceleration of the collar at B at this instant. Given: VA = 8 ft S a = 3 ft c = 2 ft
- Gear A is fixed to the crankshaft S, while gear C is fixed and gear B and the propeller are free to rotate. The crankshaft is turning with angular velocity ωs about its axis. Determine the
- The cone rolls without slipping such that at the instant shown ωz and ω'z are given. Determine the velocity and acceleration of point B at this instant. Given: (0₂ = 4 00₂ = 3 rad S rad 2 S
- If the plate gears A and B are rotating with the angular velocities shown, determine the angular velocity of gear C about the shaft DE. What is the angular velocity of DE about the y axis? Given: A =
- The right circular cone rotates about the z axis at a constant rate ω1 without slipping on the horizontal plane. Determine the magnitudes of the velocity and acceleration of points B and C.
- Rod AB is attached to a disk and a collar by ball and-socket joints. If the disk is rotating with an angular acceleration α, and at the instant shown has an angular velocity ω, determine the
- Rod AB is attached to a disk and a collar by ball-and-socket joints. If the disk is rotating at a constant angular velocity ω, determine the velocity and acceleration of the collar at A at the
- The rod BC is attached to collars at its ends by ball-and-socket joints. If disk A has angular velocity ωA, determine the angular velocity of the rod and the velocity of collar B at the instant
- The rod AB is attached to collars at its ends by ball-and-socket joints. If collar A has a speed vA, determine the speed of collar B at the instant shown. Given: VA 20 = a = 2 ft b = 6 ft ft S 8 = 45
- The rod is attached to smooth collars A and B at its ends using ball-and-socket joints. At the instant shown, A is moving with speed vA and is decelerating at the rate aA. Determine the acceleration
- Rod AB is attached to collars at its ends by using ball-and-socket joints. If collar A moves along the fixed rod with a velocity vA and has an acceleration aA at the instant shown, determine the
- The rod is attached to smooth collars A and B at its ends using ball-and-socket joints. Determine the speed of B at the instant shown if A is moving with speed vA. Also, determine the angular
- Rod AB is attached to collars at its ends by using ball-and-socket joints. If collar A moves along the fixed rod with speed vA, determine the angular velocity of the rod and the velocity of collar B
- The pendulum consists of two rods: AB is pin supported at A and swings only in the y-z plane, whereas a bearing at B allows the attached rod BD to spin about rod AB. At a given instant, the rods have
- The pendulum consists of two rods: AB is pin supported at A and swings only in the y-z plane, whereas a bearing at B allows the attached rod BD to spin about rod AB. At a given instant, the rods have
- At a given instant, rod BD is rotating about the y axis with angular velocity ωBD and angular acceleration ω'BD. Also, when θ = θ1, link AC is rotating downward such that θ' = ω2 and θ'' =
- During the instant shown the frame of the X-ray camera is rotating about the vertical axis at ωz and ω'z. Relative to the frame the arm is rotating at ωrel and ω'rel. Determine the velocity and
- At the instant shown, rod BD is rotating about the vertical axis with an angular velocity ωBD and an angular acceleration αBD. Link AC is rotating downward. Determine the velocity and acceleration
- The boom AB of the locomotive crane is rotating about the Z axis with angular velocity ω1 which is increasing at ω'1. At this same instant, θ = θ1 and the boom is rotating upward at a constant
- The locomotive crane is traveling to the right with speed v and acceleration a. The boom AB is rotating about the Z axis with angular velocity ω1 which is increasing at ω'1. At this same instant,
- At the instant shown, the arm OA of the conveyor belt is rotating about the z axis with a constant angular velocity ω1, while at the same instant the arm is rotating upward at a constant rate ω2.
- At the given instant, the rod is spinning about the z axis with an angular velocity ω and angular acceleration ω'1. At this same instant, the disk is spinning, with ω2 and ω'2 both measured
- At the instant shown, the base of the robotic arm is turning about the z axis with angular velocity ω1, which is increasing at ω'1. Also, the boom segment BC is rotating at constant rate ωBC.
- At the instant shown, the base of the robotic arm is turning about the z axis with angular velocity ω1, which is increasing at ω'1. Also, the boom segment BC is rotating with angular velociy ωBC
- The load is being lifted upward at a constant rate v relative to the crane boom AB. At the instant shown, the boom is rotating about the vertical axis at a constant rate ω1, and the trolley T is
- Determine the moments of inerta Ix and Iy of the paraboloid of revolution. The mass of the paraboloid is M. Given: M = 20 slug r = 2 ft h = 2 ft
- Determine the moment of inertia of the cylinder with respect to the a-a axis of the cylinder. The cylinder has a mass m. a a a h
- Determine the product of inertia Ixy of the body formed by revolving the shaded area about the line x = a + b. Express your answer in terms of the density ρ. Given: a = 3 ft b = 2 ft c = 3 ft
- Determine the radii of gyration kx and ky for the solid formed by revolving the shaded area about the y axis. The density of the material is ρ. Given: a = 4 ft b = 0.25 ft slug 3 ft p = 12-
- Determine the moment of inertia Iy of the body formed by revolving the shaded area about the line x = a + b. Express your answer in terms of the density ρ. Given: a = 3 ft b = 2 ft c = 3 ft
- Determine the mass moment of inertia of the homogeneous block with respect to its centroidal x' axis. The mass of the block is m. h
- Determine the elements of the inertia tensor for the cube with respect to the x, y, z coordinate system. The mass of the cube is m. X ܕܝܐ a
- Compute the moment of inertia of the rod-and-thin-ring assembly about the z axis. The rods and ring have a mass density ρ. Given: P = 2 kg m 1 = 500 mm h = 400 mm e = 120 deg
- Determine the moment of inertia of the cone about the z' axis. The weight of the cone is W, the height is h, and the radius is r. Given: W = 15 lb h = 1.5 ft r = 0.5 ft 8 = 32.2 ft 2 S
- The assembly consists of two square plates A and B which have a mass MA each and a rectangular plate C which has a mass MC. Determine the moments of inertia Ix, Iy and Iz. Given: MA = 3 kg ΜΑ Mc 0
- The bent rod has weight density γ. Locate the center of gravity G(x', y') and determine the principal moments of inertia Ix', Iy', and Iz' of the rod with respect to the x', y', z' axes. Given: Y =
- Determine the moment of inertia of the composite body about the aa axis. The cylinder has weight Wc and each hemisphere has weight Wh. Given: Wc = Wh = 10 lb b = 2 ft DO 20 lb c = 2 ft g = 322- B C
- The thin plate has a weight Wp and each of the four rods has weight Wr. Determine the moment of inertia of the assembly about the z axis. Given: Wp = 5 lb W₁ = 3 lb h = 1.5 ft a = 0.5 ft
- Rod AB has weight W and is attached to two smooth collars at its ends by ball-and-socket joints. If collar A is moving downward with speed vA when z = a, determine the speed of A at the instant z =
- The assembly consists of a rod AB of mass mAB which is connected to link OA and the collar at B by ball-and-socket joints. When θ = 0 and y = y1, the system is at rest, the spring is unstretched,
- The thin plate of mass M is suspended at O using a ball-and-socket joint. It is rotating with a constant angular velocity ω = ω1k when the corner A strikes the hook at S, which provides a permanent
- The assembly consists of a plate A of weight WA, plate B of weight WB, and four rods each of weight Wr. Determine the moments of inertia of the assembly with respect to the principal x, y, z axes.
- The assembly consists of a rod AB of mass mAB which is connected to link OA and the collar at B by ball-and-socket joints. When θ = 0 and y = y1, the system is at rest, the spring is unstretched,
- The circular plate has weight W and diameter d. If it is released from rest and falls horizontally a distance h onto the hook at S, which provides a permanent connection, determine the velocity of
- The circular disk has weight W and is mounted on the shaft AB at angle θ with the horizontal. Determine the angular velocity of the shaft when t = t1 if a constant torque M is applied to the shaft.
- The plate of weight W is subjected to force F which is always directed perpendicular to the face of the plate. If the plate is originally at rest, determine its angular velocity after it has rotated
- The circular disk has weight W and is mounted on the shaft AB at angle of θ with the horizontal. Determine the angular velocity of the shaft when t = t1 if a torque M = M0ebt applied to the shaft.
- The space capsule has mass mc and the radii of gyration are kx = kz and ky. If it is traveling with a velocity vG, compute its angular velocity just after it is struck by a meteoroid having mass mm
- The rod assembly is supported by journal bearings at A and B, which develops only x and z force reactions on the shaft. If the shaft AB is rotating in the direction shown with angular velocity ω,
- The rod assembly is supported by journal bearings at A and B, which develops only x and z force reactions on the shaft. If the shaft AB is subjected to a couple moment M0j and at the instant shown
- The rod AB supports the sphere of weight W. If the rod is pinned at A to the vertical shaft which is rotating at a constant rate ωk, determine the angle θ of the rod during the motion. Neglect the
- The conical pendulum consists of a bar of mass m and length L that is supported by the pin at its end A. If the pin is subjected to a rotation ω, determine the angle θ that the bar makes with the
- The rod AB supports the sphere of weight W. If the rod is pinned at A to the vertical shaft which is rotating with angular acceleration α k, and at the instant shown the shaft has an angular
- The thin rod has mass mrod and total length L. Only half of the rod is visible in the figure. It is rotating about its midpoint at a constant rate θ', while the table to which its axle A is fastened
- The cylinder has mass mc and is mounted on an axle that is supported by bearings at A and B. If the axle is turning at ωj, determine the vertical components of force acting at the bearings at this
- The cylinder has mass mc and is mounted on an axle that is supported by bearings at A and B. If the axle is subjected to a couple moment M j and at the instant shown has an angular velocity ωj,
- A thin rod is initially coincident with the Z axis when it is given three rotations defined by the Euler angles φ, θ, and ψ. If these rotations are given in the order stated, determine the
- The propeller on a single-engine airplane has a mass M and a centroidal radius of gyration kG computed about the axis of spin. When viewed from the front of the airplane, the propeller is turning
- While the rocket is in free flight, it has a spin ωs and precesses about an axis measured angle θ from the axis of spin. If the ratio of the axial to transverse moments of inertia of the rocket is
- The rotor assembly on the engine of a jet airplane consists of the turbine, drive shaft, and compressor. The total mass is mr, the radius of gyration about the shaft axis is kAB, and the mass center
- An airplane descends at a steep angle and then levels off horizontally to land. If the propeller is turning clockwise when observed from the rear of the plane, determine the direction in which the
- The conical top has mass M, and the moments of inertia are Ix = Iy and Iz. If it spins freely in the ball-and-socket joint at A with angular velocity ωs compute the precession of the top about the
- The toy gyroscope consists of a rotor R which is attached to the frame of negligible mass. If it is observed that the frame is precessing about the pivot point O at rate ωp determine the angular
- The top has weight W and can be considered as a solid cone. If it is observed to precessing about the vertical axis at a constant rate of ωy, determine its spin ωs. Given: W = 3 lb rad Oy = 5 S 8 =
- The projectile has a mass M and axial and transverse radii of gyration kz and kt, respectively. If it is spinning at ωs when it leaves the barrel of a gun, determine its angular momentum. Precession
- The disk of mass M is thrown with a spin ωz. The angle θ is measured as shown. Determine the precession about the Z axis. Given: M = 4 kg 8 = 160 deg r = 125 mm = 6 rad S
- A spring has stiffness k. If a block of mass M is attached to the spring, pushed a distance d above its equilibrium position, and released from rest, determine the equation which describes the
- If the lower end of the slender rod of mass M is displaced a small amount and released from rest, determine the natural frequency of vibration. Each spring has a stiffness k and is unstretched when
- A weight W is suspended from a spring having a stiffness k. If the weight is given an upward velocity of v when it is distance d above its equilibrium position, determine the equation which describes
- When a block of mass m1 is suspended from a spring, the spring is stretched a distance δ. Determine the natural frequency and the period of vibration for a block of mass m2 attached to the same
- Determine to the nearest degree the maximum angular displacement of the bob if it is initially displaced θ0 from the vertical and given a tangential velocity v away from the vertical. Given: 80 =
- The semicircular disk has weight W. Determine the natural period of vibration if it is displaced a small amount and released. Given: W = 20 lb r = 1 ft 8 = 32.2 ft 2
- The square plate has a mass m and is suspended at its corner by the pin O. Determine the natural period of vibration if it is displaced a small amount and released.
- The pointer on a metronome supports slider A of weight W, which is positioned at a fixed distance a from the pivot O of the pointer. When the pointer is displaced, a torsional spring at O exerts a
- While standing in an elevator, the man holds a pendulum which consists of cord of length L and a bob of weight W. If the elevator is descending with an acceleration a, determine the natural period of
- The disk, having weight W, is pinned at its center O and supports the block A that has weight WA. If the belt which passes over the disk is not allowed to slip at its contacting surface, determine
- The spool of weight W is attached to two springs. If the spool is displaced a small amount and released, determine the natural period of vibration. The radius of gyration of the spool is kG. The
- The disk, having weight W, is pinned at its center O and supports the block A that has weight WA. If the belt which passes over the disk is not allowed to slip at its contacting surface, determine
- The semicircular disk has weight W. Determine the natural period of vibration if it is displaced a small amount and released. Solve using energy methods. Given: W = 20 lb r = 1 ft = 8-3222/22 S
- The bar has length l and mass m. It is supported at its ends by rollers of negligible mass. If it is given a small displacement and released, determine the natural frequency of vibration. R B
- The square plate has a mass m and is suspended at its corner by the pin O. Determine the natural period of vibration if it is displaced a small amount and released. Solve using energy methods.
- The uniform rod of mass m is supported by a pin at A and a spring at B. If the end B is given a small downward displacement and released, determine the natural period of vibration. B
- The disk of mass M is pin-connected at its midpoint. Determine the natural period of vibration of the disk if the springs have sufficient tension in them to prevent the cord from slipping on the disk
- Determine the differential equation of motion of the block of mass M when it is displaced slightly and released. The surface is smooth and the springs are originally unstretched. Given: M = 3 kg k =
- Determine the natural period of vibration of the sphere of mass M. Neglect the mass of the rod and the size of the sphere. Given: M = 3 kg k = 500 ZIE m a = 300 mm b = 300 mm
- Determine the natural frequency of vibration of the disk of weight W. Assume the disk does not slip on the inclined surface. Given: W = : 20 lb
- The slender rod has a weight W. If it is supported in the horizontal plane by a ball-and-socket joint at A and a cable at B, determine the natural frequency of vibration when the end B is given a
- If the disk has mass M, determine the natural frequency of vibration. The springs are originally unstretched. Given: M = 8 kg N k = 400 r = 100 mm
- Use a block-and-spring model like that shown in Fig. 22-14a but suspended from a vertical position and subjected to a periodic support displacement of δ = δ0 cos ωt, determine the equation of
- The block of weight W is attached to a spring having stiffness k. A force F = F0 cosω t is applied to the block. Determine the maximum speed of the block after frictional forces cause the free
- Determine the differential equation of motion of the spool of mass M. Assume that it does not slip at the surface of contact as it oscillates. The radius of gyration of the spool about its center of
- If the block is subjected to the impressed force F = F0 cos(ωt), show that the differential equation of motion is y'' + (k/m)y = (F0/m)cos(ωt), where y is measured from the equilibrium position of
- Draw the electrical circuit that is equivalent to the mechanical system shown. What is the differential equation which describes the charge q in the circuit? wwww 4 m