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# Rotation

A rotation is a curler movement of an object around a center of rotation. A 3-D object rotates around an imaginary line called a rotation axis. It this axis is within the body and passes through its center of mass the body will rotate upon itself or spin. A rotation about an external point is called a revolution when it is produced by gravity.

A rotation is a rigid body movement which is unlike a translation which keeps a point fixed. All rigid body movements are rotations, translation or combination of the two. A rotation is a progressive radial orientation to a common point. The distinction between a rotation and an orbit is the location of the axis of the rotation.

Rotations around the x, y, and z axes are called principal rotations. Rotations around any axis can be performed by taking a rotation around the x axis, followed by a rotation around the y axis, followed by the rotation around the z axis.

The speed of rotation is given by angular frequency. The time-rate of change of angular frequency is angular acceleration. Said change is caused by torque. According to the right-hand rule, the direction away from the observer is associated with clockwise rotation and the direct towards the observer with counter-clockwise rotation.

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Explain in detail the concept of center of mass of a system of bodies or a rigid body with solved examples.

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Explain the concept of Moment of Inertia of a rotating body with examples.

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Explain how using isospin invariance one can compute the ratio of some decay rates of the Kaons.

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A uniform cylinder is allowed to roll down the track. Assume the cylinder rolls without slip, with r_1 = 1.0 m and R_2 = 0.04 m. What is the minimum value of h such that the cylinder never leaves the surface of the track? How would the height change if the object is a sphere? See the attached file.

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A uniform 25 kg disc with a diameter of 9 meters is mounted on a frictionless axle at its center. The disc is rotating at 2.2rad/s, up. A person (85kg) is initially at its center. The person then walks out to the edge of the disc, facing forward, and catches a 2.5kg ball tossed in his face at 18m/s with respect to the ground.

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Please see the attached file for diagram. A designer wishes to make a clock with a pendulum in the shape of a flat disk. Instead of swinging from the end of a rod, however, the disk is to pivot about a point between its center of mass and its rim. If the disk has a radius of 15.0 cm and its intended period of oscillation

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See attached file. Determine the direction of rotation of the armature for the current and field directions. Show lines of force.

### Linear Motion and Radial Acceleration of the Helecopter

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How and why does a day measured with respect to the Sun differ from a day measured with respect to the stars?

### Eigenvectors of spin operators of a spin 1/2 system

See attached file.

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