The rotor (flywheel) of a loy gyroscope has mass 0.140 kg. Its moment of inertia about its axis is 1.20 × 10 −4 kg · m 2 . The mass of the frame is 0.0250 kg. The gyroscope is supported on a single pivot ( Fig. E10.51 ) with its center of mass a horizontal distance of 4.00 cm from the pivot. The gyroscope is processing in a horizontal plane at the rate of one revolution in 2.20 s. (a) Find the upward force exerted by the pivot, (b) Find the angular speed with which the rotor is spinning about its axis, expressed in rev/min. (c) Copy the diagram and draw vectors lo show the angular momentum of the rotor and the torque acting on it. Figure E10.51
The rotor (flywheel) of a loy gyroscope has mass 0.140 kg. Its moment of inertia about its axis is 1.20 × 10 −4 kg · m 2 . The mass of the frame is 0.0250 kg. The gyroscope is supported on a single pivot ( Fig. E10.51 ) with its center of mass a horizontal distance of 4.00 cm from the pivot. The gyroscope is processing in a horizontal plane at the rate of one revolution in 2.20 s. (a) Find the upward force exerted by the pivot, (b) Find the angular speed with which the rotor is spinning about its axis, expressed in rev/min. (c) Copy the diagram and draw vectors lo show the angular momentum of the rotor and the torque acting on it. Figure E10.51
The rotor (flywheel) of a loy gyroscope has mass 0.140 kg. Its moment of inertia about its axis is 1.20 × 10−4 kg · m2. The mass of the frame is 0.0250 kg. The gyroscope is supported on a single pivot (Fig. E10.51) with its center of mass a horizontal distance of 4.00 cm from the pivot. The gyroscope is processing in a horizontal plane at the rate of one revolution in 2.20 s. (a) Find the upward force exerted by the pivot, (b) Find the angular speed with which the rotor is spinning about its axis, expressed in rev/min. (c) Copy the diagram and draw vectors lo show the angular momentum of the rotor and the torque acting on it.
Figure E10.51
Definition Definition Product of the moment of inertia and angular velocity of the rotating body: (L) = Iω Angular momentum is a vector quantity, and it has both magnitude and direction. The magnitude of angular momentum is represented by the length of the vector, and the direction is the same as the direction of angular velocity.
two satellites are in circular orbits around the Earth. Satellite A is at an altitude equal to the Earth's radius, while satellite B is at an altitude equal to twice the Earth's radius. What is the ratio of their periods, Tb/Ta
Fresnel lens: You would like to design a 25 mm diameter blazed Fresnel zone plate with a first-order power of
+1.5 diopters. What is the lithography requirement (resolution required) for making this lens that is designed
for 550 nm? Express your answer in units of μm to one decimal point.
Fresnel lens: What would the power of the first diffracted order of this lens be at wavelength of 400 nm?
Express your answer in diopters to one decimal point.
Eye: A person with myopic eyes has a far point of 15 cm. What power contact lenses does she need to correct
her version to a standard far point at infinity? Give your answer in diopter to one decimal point.
Paraxial design of a field flattener. Imagine your optical system has Petzal curvature of the field with radius
p. In Module 1 of Course 1, a homework problem asked you to derive the paraxial focus shift along the axis
when a slab of glass was inserted in a converging cone of rays. Find or re-derive that result, then use it to
calculate the paraxial radius of curvature of a field flattener of refractive index n that will correct the observed
Petzval. Assume that the side of the flattener facing the image plane is plano. What is the required radius of
the plano-convex field flattener? (p written as rho )
Chapter 10 Solutions
University Physics with Modern Physics (14th Edition)
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