CALC The balance wheel of a watch vibrates with an angular amplitude Θ. angular frequency ω , and phase angle ϕ = 0. (a) Find expressions for the angular velocity dθ/dt and angular acceleration d 2 θ / dt 2 as functions of time. (b) Find the balance wheel’s angular velocity and angular acceleration when its angular displacement is Θ, and when its angular displacement is Θ/2 and θ is decreasing. ( Hint: Sketch a graph of θ versus t .)
CALC The balance wheel of a watch vibrates with an angular amplitude Θ. angular frequency ω , and phase angle ϕ = 0. (a) Find expressions for the angular velocity dθ/dt and angular acceleration d 2 θ / dt 2 as functions of time. (b) Find the balance wheel’s angular velocity and angular acceleration when its angular displacement is Θ, and when its angular displacement is Θ/2 and θ is decreasing. ( Hint: Sketch a graph of θ versus t .)
CALC The balance wheel of a watch vibrates with an angular amplitude Θ. angular frequency ω, and phase angle ϕ = 0. (a) Find expressions for the angular velocitydθ/dt and angular accelerationd2θ/dt2 as functions of time. (b) Find the balance wheel’s angular velocity and angular acceleration when its angular displacement is Θ, and when its angular displacement is Θ/2 and θ is decreasing. (Hint: Sketch a graph of θ versus t.)
Definition Definition Rate of change of angular velocity. Angular acceleration indicates how fast the angular velocity changes over time. It is a vector quantity and has both magnitude and direction. Magnitude is represented by the length of the vector and direction is represented by the right-hand thumb rule. An angular acceleration vector will be always perpendicular to the plane of rotation. Angular acceleration is generally denoted by the Greek letter α and its SI unit is rad/s 2 .
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 14 Solutions
University Physics with Modern Physics (14th Edition)
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