(a) Show that the position of a particle on a circle of radius R with its center at the origin is r → = R (cos θî + sin θĵ ), where θ is the angle the position vector makes with the x -axis. (b) If the particle moves with constant speed v starting on the x -axis at t = 0, find an expression for θ in terms of time t and the period T to complete a full circle, (c) Differentiate the position vector twice with respect to time to find the acceleration, and show that its magnitude is given by Equation 3.16 and its direction is toward the center of the circle.
(a) Show that the position of a particle on a circle of radius R with its center at the origin is r → = R (cos θî + sin θĵ ), where θ is the angle the position vector makes with the x -axis. (b) If the particle moves with constant speed v starting on the x -axis at t = 0, find an expression for θ in terms of time t and the period T to complete a full circle, (c) Differentiate the position vector twice with respect to time to find the acceleration, and show that its magnitude is given by Equation 3.16 and its direction is toward the center of the circle.
(a) Show that the position of a particle on a circle of radius R with its center at the origin is
r
→
= R(cos θî + sin θĵ), where θ is the angle the position vector makes with the x-axis. (b) If the particle moves with constant speed v starting on the x-axis at t = 0, find an expression for θ in terms of time t and the period T to complete a full circle, (c) Differentiate the position vector twice with respect to time to find the acceleration, and show that its magnitude is given by Equation 3.16 and its direction is toward the center of the circle.
Imagine you are out for a stroll on a sunny day when you encounter a lake. Unpolarized light from the sun is reflected off the lake into your eyes. However, you notice when you put on your vertically polarized sunglasses, the light reflected off the lake no longer reaches your eyes. What is the angle between the unpolarized light and the surface of the water, in degrees, measured from the horizontal? You may assume the index of refraction of air is nair=1 and the index of refraction of water is nwater=1.33 . Round your answer to three significant figures. Just enter the number, nothing else.
Applications and Investigations in Earth Science (9th Edition)
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