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(A) Find the moment of inertia of a uniform plate shaped like a quarter of a circle of radius R, made to rotate around the square corner (with the rotation axis perpendicular to the plate). Suggestion: have the plate be in the first quadrant (that is, the square corner is the origin) and do the integral in polar coordinates. Express this both in terms of its radius and mass density, and its radius and mass.
(B) The same uniform quarter-circle plate, now made to rotate around an axis that is along one of its straight sides. This one is easier in polar coordinates, but can be done in rectangular coordinates as well. Again, express this both in terms of radius and mass density, and in terms of radius and mass.
The electric field at point P just outside the outer surface of a hollow spherical conductor of inner radius 15 cm and outer radius 31 cm has magnitude 465 N/C and is directed outward.
A flat sheet of sodium chloride has a thickness of 2.50 cm. It is on top of a flat sheet of fused quartz that has a thickness of 1.26 cm, how far (in cm) would it have traveled in a vacuum
A solid wheel (solid cylinder) with mass 2.5 kg and a radius of 0.50 meter starts rotating from rest and has a constant angular acceleration of 2.5 radians/second^2 Determine the torque required to produce this motion
Three charges are on the y-axis. Two of the charges, each ?2q, are locatedy=±d, and the third charge, +4q, Derive an expression for the electric field at a point P on the x-axis
A 240g block is attached to a horizontal spring and executes simple harmonic motion with a period of 0.150 s. If the total energy of the system is 3J.
The portion of the board on the table measures .30m and the portion of the table measures .20m. Explain how far can the center of the box be over the table before the board begins to tilt?
A 2.75-gram air inflated balloon is given an excess negative charge, q1 = -3.00 × 10-8 C, by rubbing it with a blanket. It is found that a charged rod can be held above the balloon at a distance of d = 5.20 cm to make the balloon float. In order f..
A bird, starting from its nest (we'll call that the origin), flies 24.0 km due southeast. It then changes directions and flies 26.0 km in a direction 60° north of east. Find the magnitude and direction of its resultant displacement.
What is the charge density on the surface. suppose that air resistance can be neglected.
A coil of 15 turns and radius 10.0 cm surrounds a long solenoid of radius 2.00 cm and 1000 turns/meter. The current in the solenoid changes as I = (5.00 A) sin(120t). Find the induced emf in the 15-turn coil as a function of time.
Two parallel wires of length 17 m are separated by a distance of a = 0.13 cm, What is the magnetic force on each wire
Coefficient of linear expansion for aluminium
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