What is the velocity center of mass
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Q: Review Conceptual Example 2 before attempting this problem. The moon has a diameter of 3.48 x 106 m…
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The Earth is 1.5 × 1011 m from the Sun and takes a year to make one complete orbit. It rotates on its own axis once per day. It can be treated approximately as a uniform-density sphere of mass 6 × 1024 kg and radius 6.4 × 106 m (actually, its center has higher density than the rest of the planet, and the Earth bulges out a bit at the equator). Using this crude approximation, calculate the following. What is the velocity center of mass?
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- The Moon has an interesting relationship with the Earth, where the same face of the Moon is always facing towards the Earth. This is called tidal locking, where the time it takes for the Moon to rotate once is exactly equal to the time it takes for it to orbit the Earth. Given that the Moon performs 13.5 rotations per year, and that the Earth has a mass of 5.97 1024 kg, find the center to center distance between the Earth and the X Moon. You must show your work in order to obtain credit. The gravitational constant is G = 6.67 x 10 11 Nm kg2Consider a rod of total length 4 m that is free to pivot above its center. The linear mass density of the rod is given by λ(x) = 6 x4 (kg/m), where x is the distance from the center of the rod. The rod is in outer space, so you don't have to worry about any gravitational torques. There is a 168 N force that acts perpendicularly to the rod at its right end, and there is a 512 N force that acts halfway between the left end of the rod and its center. This force acts at an angle of 33 degrees to the vertical. This scenario is shown below: Calculate the angular acceleration of the rod, in rad/s2. The answer could be positive or negative. (Please answer to the fourth decimal place - i.e 14.3225)Problem 3: Microwave ovens rotate at a rate of about 5.8 rev/min. Randomized Variables f = 5.8 rev/min Part (a) What is this in revolutions per second? Numeric : A numeric value is expected and not an expression. f = Part (b) What is the angular velocity of this microwave in radians per second? Numeric : A numeric value is expected and not an expression. W =
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- A neutron star is the remnant of a large star that exploded in a supernovaat the end of its life. Suppose the star’s radius decreases by a factor of6 × 10−5 during this process, and its mass decreases by a factor of eight.If the star rotates once per 20 days during its life, how fast would itsremnant neutron star rotate? Assume the star is always a solid, uniformsphere. (It is not, but this exercise still gives a reasonable answer).Earth is rotating about the Sun in our solar system. The distance between the Earth and Sun is 1.5 x 10'm. Consider the impact of an asteroid of mass 8.9 x1015 kg and a speed of 90,000 km/h with respect to the Earth's surface. The asteroid strikes the Earth at the equator as shown in Figure. Consider the mass and radius of thec Earth are ME 5.97 x 10 kg and R: = 6.38 x10° m, respectively. Assume that the axial and orbital axis of rotations are parallel to cach other. %3D Earth North Pole (d) How much encrgy is needed to stop the Earth's rotation about its axis after the collision? (e) What would be the moment of inertia of the Earth if the axis of rotation is parallelly shifted so that it touches the cquator?A solid ball ( I = 2/5 mr2 ) a mass of 2 kg and a radius of 4 cm is rolling (moves both translationally and rotationally) from rest down the top of the plane an incline whose height is 7 m, the angle of inclination is 45o (sin 45o = 0.7). Define the speed of the ball when it reaches the foot of the incline! (It is known that the acceleration due to gravity by 10 ms-2 .)