The scientist Archimedes is famed to have once said “Give me a lever long enough and I’ll move the world”. Let us assume that Archimedes is approximately (60 kg) and the world has a mass of approximately (6×1024kg). If the fulcrum of our lever is (1 m) away from the Earth’s side, how long is our lever? (Assume that all of this takes place on an infinite plane with Earth surface gravity.) (Give your answer in units of the distance to the galaxy Andromeda which is 770 kpc away. You will need to convert from meters.)

Q: In an experiment where we will use a vertically-mounted turntable that has a hub attached at its…

A: To explain: The effect of the diameter of the string have on the lever arm.

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A: Let, the mass of the rods be 'M' and length of the rods be 'L' , moment of inertia of the rod having…

Q: A typical small rescue helicopter has four blades: Each blade is 4.00 m long and has a mass of 50.0…

A: Introduction:       Moment of inertia (I) = mass ×distance 2…

Q: how fast will the station be spinning?

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A:

Q: A Ferris wheel has diameter of 10 m and makes one revolution in 8.0 seconds. A person weighing 6 N…

A: Given:- The Ferris wheel has a diameter of d = 10 m  The time for the revolution  t= 8 second…

Q: Consider a non-rotating space station in the shape of a long thin uniform rod of mass 6.85 x 10^6 kg…

A: the mass of space station , m = 6.85 * 10^6 kg the length , l = 1476 m force applied , F = 4.65 *…

Q: Consider a non-rotating space station in the shape of a long thin uniform rod of mass 7.38 x 10^6 kg…

A:

Q: Suppose a star the size of our Sun, but with mass 5.0 times as great, were rotating at a speed of…

A: Introduction: Here in this problem we use conservation of angular momentum.  For system of masses⇒…

Q: Consider a non-rotating space station in the shape of a long thin uniform rod of mass 1.68 x 10^6 kg…

A:

Q: tire has 212,000 revolutions in one day and three hours. What is the speed in radian per second?

A: Solution

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A:

Q: If planet Earth has a radius of 6,378 X106m, how much is the tangential speed of a person located at…

A: Radius of earth (R)=6.378×106 m Mass of the person (m)=62.7 kg Time period of earth's rotation…

Q: The rotor of an electric motor has rotational inertia Im =2.0 * 10-3 kg  m2 about its central axis.…

A:

Q: Take the radius of the Earth to be 6309 km. The angular speed of a point on Earth’s surface at…

A: Given latitude 30° Radius - 6309 km

Q: before shutting off, then how fast will the station be rotating when the engines stop?

A:

Q: The diameter of a bicycle wheel is 60 centimeters. How far does the wheel travel when it makes 35…

A:

Q: A 1.0- kg mass is attached to a string wrapped around a shaft of negligible mass and having a 4.0-…

A: Given: The mass attached to the string is 1.00 kg. The height of this mass is 1.3 m. The speed…

Q: A rod of length 1.21 m and mass 4.3 kg can freely rotate around uppermost point (see Fig). A bullet…

A: According to question--- Given data-- length of road L = 1.21 m. mass of road = 4.3 kg. mass of…

Q: The figure below shows a sphere of mass 4 kg attached to a horizontal rod by two strings of equal…

A: This question can be solved by applying the basic concepts of circular motion.

Q: Consider an "L-shaped rod” of uniform mass density, hinged at point 'O' is held at rest…

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Q: A certain planet spins on its axis 4 a day and orbits the sun 57 a year. Determine the average…

A: To determine: The average angular velocity (rad/s) of the earth as it spins on its axis. Given that,…

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Q: The speed of a person standing on the equator, due to the earth's rotation.

A:

Q: A uniform horizontal disc has a point mass of 70 kg placed on its edge. The system rotates about a…

A: point mass = 70 kg original frequency = 12 HzFinal frequency = 30 Hz

Q: Evaluate the centroid (x,5) of the compound wire as measured from the origin O (0,0) in FIGURE 4.…

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Q: If the Earth , supposed to be a uniform sphere contracts slightly so that its radius becomes less by…

A: The relations between the time period will be

Q: Consider a non-rotating space station in the shape of a long thin uniform rod of mass 1.84 x 10^6 kg…

A:

Q: Consider a non-rotating space station in the shape of a long thin uniform rod of mass 4.08 x 10^6 kg…

A:

Q: Please show your work. Thank you! 81. A certain planet spins on its axis 2 a day and orbits the sun…

A: Given value--- time taken by planet = 2 a day. we have to find --- angular velocity ?

Q: You are performing an experiment out in space, assume you are far from any large planets. You have a…

A: first mass = 100 kg Length of rod = 5 m M = 10,000 kg d = 0.05 m

Q: A giant wheel, 40 m in diameter, is fitted with a cage and platform on which a man can stand. The…

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Q: if I'm doing an experiment about one dimension motion on an inclined track with a cart, and get…

A: Given that: Acceleration values found: g1=8.79 m/s2 .....(10% error)g2=8.66 m/s2  ......(12%…

Q: A 1.0- kg mass is attached to a string wrapped around a shaft of negligible mass and having a 8.0-…

A: The total energy of the sytem must be conserved. The initial energy of the sytem is equal to the…

Q: bowling ball, whose radius R is 11 cm and whose mass is 7.2 kg. rolls from rest down a plank whose…

A:

Q: A 6 - m string wounded on the rim of a wheel (r = 10.28 cm) is being pulled out at a rate of 61…

A: length of string (L) = 6 m radius (r) = 10.28 cm= 0.1028 m v = 61 cmsec= 0.61 ms

Q: A conical pendulum, as shown in the figure, is 12 meter long. a ball of 56 kg tied to the end of a…

A:

Q: Round objects are made, each with the same mass and radius but a different distribution of mass.…

A: To solve the given question, we need to use the concept of moment of inertia, the higher the moment…

Q: Consider a non-rotating space station in the shape of a long thin uniform rod of mass 9.84 x 10^6 kg…

A:

Q: What is the angle (in radians) between the vectors (1.3, -2.2, 7.1) and (1.9, 5.2, -10.0)?

A:

Q: Consider a non-rotating space station in the shape of a long thin uniform rod of mass 6.07 x 10^6 kg…

A:

Q: Consider a non-rotating space station in the shape of a long thin uniform rod of mass 1.09 x 10^6 kg…

A: Given  Mass , m = 1.09×106 kg  Length , L = 769 m  Force , F =1.79×105 N  Time , t = 74 sec. Moment…

Q: Consider a non-rotating space station in the shape of a long thin uniform rod of mass 7.62 x 10^6 kg…

A: Given : Mass of rod=M=7.62x106 kg Length of rod=L=1075 m Force=F=5.04x105 N Time=t=139 s=2.32 min

Q: accelerates uniformly in 4.0 seconds from rest, what is its angular acceleration in radians per…

A: The CD makes 500 rev per minute Number of revolutions per second is  500/60 = 50/6 = 25/3  revs/sec…

Q: What is the angle between the vectors a = (10, -10, 0) and b = (-5, 5, 2), in radians?

A: Given data: Vector a = (10, - 10, 0) Vector B = (-5, 5, 2) Required: Angle between the vectors

Q: Consider a non-rotating space station in the shape of a long thin uniform rod of mass 6.85 x 10^6 kg…

A: the mass of space station , m = 6.85 * 10^6 kg the length , l = 1476 m force applied , F = 4.65 *…

Central Force

Central force is the force that acts along the center of mass of one body to the center of mass of another body. Its direction from or away from a point on a body to another is called the center of the force. Such forces include gravitational force between two massive objects or electrostatic forces between two charged particles. So from atoms to planets, the central forces play an important role in shaping our daily lives. One of the remarkable features of central forces is that they are conservative, i.e. the total energy of a central force system can always be expressed as a gradient of a potential energy function.