Repeat Problem 87, now generalizing to the case where not only the speed but also the radius may be changing. 87. In dealing with nonuniform circular motion, as shown in Fig. 3.23, we should write Equation 3.16 as a r = v 2 / r , to show that this is only the radial component of the acceleration. Recognizing that v is the object’s speed, which changes only in the presence of tangential acceleration, differentiate this equation with respect to time to find a relation between the magnitude of the tangential acceleration and the rate of change of the magnitude of the radial acceleration. Assume the radius stays constant.
Repeat Problem 87, now generalizing to the case where not only the speed but also the radius may be changing. 87. In dealing with nonuniform circular motion, as shown in Fig. 3.23, we should write Equation 3.16 as a r = v 2 / r , to show that this is only the radial component of the acceleration. Recognizing that v is the object’s speed, which changes only in the presence of tangential acceleration, differentiate this equation with respect to time to find a relation between the magnitude of the tangential acceleration and the rate of change of the magnitude of the radial acceleration. Assume the radius stays constant.
Repeat Problem 87, now generalizing to the case where not only the speed but also the radius may be changing.
87. In dealing with nonuniform circular motion, as shown in Fig. 3.23, we should write Equation 3.16 as ar = v2/r, to show that this is only the radial component of the acceleration. Recognizing that v is the object’s speed, which changes only in the presence of tangential acceleration, differentiate this equation with respect to time to find a relation between the magnitude of the tangential acceleration and the rate of change of the magnitude of the radial acceleration. Assume the radius stays constant.
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.
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