(Please refer attachment for detailed problem description)

Problem 1 : The 40 kg disc is released from rest with the spring compressed. At the instant shown (see attachment) it has a speed of 4 m/s and the spring is unstretched. From this poinr determine the distance d that the disc moves down the 30 degree ramp before momentarily stopping. The disc rolls without slipping. Determine :

a) The distance d in meters down the ramp from point A.
b) The moment of inertia of the disc about G in kgm^2
c) The angular velocity of the disc in rad/sec at this instant.
d) The work done by the spring in Nm during the downward motion.
e) The distance h in m, up the ramp from A to the starting point.

Problem 2 : A 5 kg uniform rod 800mm long rotates about pin B in a vertical plane. If the rod is released from rest when it is horizontal, determine :

a) Moment of inertia of the rod about B in kg m^2.
b) Angular velocity of the rod in rad/sec when vertical.
c) Angular velocity of the rod in kg m^2 at theta = 75 degrees
d) X direction support reaction in N at pin B at theta = 75 degrees
e) Y direction support reaction in N at pin B at theta = 75 degrees

The rigidbody shown in this diagram is moving such that the velocities of points A and B are the same. The magnitude of the velocity of point A is 25m/s and the distance between points A and B is 10m.
Determine the magnitude of the angular velocity of the rigidbody.
Express your answer in rad/s and give you answer to 4

A rigidbody consists of six particles, each of mass m, fixed tot he ends of three light rods of length 2a, 2b, and 2c, respectively, the rods being held mutually perpendicular to one another at their midpoints.
a) Show that a set of coordinate axes defined by the rods are principal axes, and write down the inertia tensor for

** Please see the attachment for the complete problem description **
A rigidbody is spinning with an angular speed of 60pie radians per second (1800 rpm). The axis of rotation lies in the direction of the vector 2i + 2j -k. A small particle on the spinning body with mass of one kilogram passes through the point P with positi

Please solve problems 6/140 and 6/127 only. Refer attachment for fig.
Problem 6/140 : The sheave of 400 mm radius has a mass of 50 kg and a radius of gyration of 300 mm. The sheave and its 100 kg load are suspended by the cable and the spring which has a stiffness of 1.5 kN/m. If the system is released from rest with the spri

Problem 1 : To determine moment of inertia about different axes of rotation of a circular disc of given radius of gyration.
Problem 2 : A two pulley system. To determine acceleration, tension in the cable etc.

1. The vector expression of an acceleration can be obtained by:
a. Differentiation position vector once
b. Differentiation velocity vector once
c. Differentiation position vector three times
d. Differentiation velocity vector twice
2. The work of forces acting on a rigidbody can be expressed as:
a. the dot product

The earth maybe considered as a rigid axisymmetric body with a small quadrupole deformation. (There are two problems (a) and (b))
(a) If the exterior gravitational potential is written as:
V(r)=-M_e*G*1/r*[1-J(R_e/r)^2* P_2(costheta)]
Here, M_e is the mass of the earth, R_e is the equatorial radius and theta the colatit

Please do probs 6/148 and 6/136 only. Refer attachment for fig.
Problem 6/148 : The fig. shows cross section of a garage door which is a uniform rectangular panel 8 x 8 ft ans weighing 200 lb. The door carries two spring assemblies, one on each side of the door, like the one shown. Each spring has a stiffness of 50 lb/ft, and

Explain why the work required to pull a dynamics cart up an incline, in the absence of friction, should be the same as the work required to lift the cart vertically through the vertical displacement it experiences in the process.

A bead slides on a smooth rigid wire bent into the form of a circular loop of radius b. If the plane of the loop is vertical and if the bead starts from rest at a point that is level with the center of the loop, find the speed of the bead at the bottom and the reaction of the wire on the bead at that point.