A spinning sphere has rotational kinetic energy given by E = mR²w² where m is the (constant) mass of the sphere, R is the radius of the sphere, and w is its angular speed (measured in radians per second). If the energy remains constant, use differentials to estimate the change in angular speed that corresponds to a 1% decrease in the radius of the sphere.

Q: Rutherford fired a beam of alpha particles (helium nuclei) at a thin sheet of gold. An alpha…

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Q: Neurons in our bodies carry weak currents that produce detectable magnetic fields. A technique…

A: Given:-  The magnetic field is B = 1.0 x 10-15 T  The distance from the neuron is d = 2.9 cm  Find:-…

Q: Assume the three blocks (m₁ = 1.0 kg, m₂ = 2.0 kg, and m3 = 3.5 kg) portrayed in the figure below…

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Q: 8. A heating element using nichrome connected to a 230 V supply draws an initial current of 3.2 A…

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Q: 1. A 200-kg cylinder is hung by means of two cables AB and AC, which are attached to the top of a…

A: Given, mass of the cylinder, m = 200 kg

Q: The figure below represents the top view of a cubic gaussian surface in a uniform electric field E…

A: As per guidelines only 3 subparts are solved here.

Q: Initial Angular Momentum (J-s)

A: The angular momentum of a rigid object is the product of its moment of inertia and its angular…

Q: (a) A particle with charge g is located a distance d from an infinite plane. Determine the electric…

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Q: A cart filled with sand rolls at a speed of vcart = 1.4 m/s along a horizontal path without…

A: The incident is perfect example of inelastic collision. if two masses of M1 and M2 with their…

Q: 1. The vector v and its initial point are given. Find the terminal point. v = (4, -9); Initial…

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Q: ic: You are an astronaut on the international space station. As you're unpacking the most recent…

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Q: How far from a 6.50 µC point charge will the potential be 170 V?  m At what distance will it be 3.40…

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Q: For a receding sound source, the frequency will __________ while the wavelength will __________. The…

A: Consider the speed of sound is v and the speed of the source is vs.

Q: The 2.90 kg cube in the figure has edge lengths d = 6.00 cm and is mounted on an axle through its…

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Q: Three point charges are arranged as shown in the figure below. (a) Find the vector electric field…

A: Given data, The positive charge q1=5.5 nC=5.5×10-9 C The negative charge q2=-3 nC=-3×10-9 C The test…

Q: An electric drill starts from rest and undergoes uniform angular acceleration for a period of 0.180…

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Q: 2- A velocity vector is 20 m/s South 60° East. What are the components of this vector

A: Given:  Velocity vector: 20m/s South 60∘ East. To determine: Components of vector

Q: 13. The frequency of a photon having energy 100 eV is (Take h = 6.62 × 10-³4 J s; 1 eV = 1.6 × 10-¹⁹…

A: The question is The answer is  The explanation is as follows

Q: Assume the magnitude of the electric field on each face of the cube of edge L = 1.04 m in the figure…

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Q: 11- A toy car (200 g) moves by shooting a plastic ball (50 gr horizontally out the back. The average…

A: (a) Free body diagram of toy car A. and ball B

Q: Water is flowing through a 1 foot chamber pipe at the rate of 10 ft./sec. What is the volume flow of…

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Q: A bicyclist starting at rest produces a constant angular acceleration of 1.30 rad/s2 for wheels that…

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Q: There is a free neutron that is at rest. It decays into a proton (mass energy is 938.30 MeV), an…

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Q: A projectile is fired at ?0=433.0 m/s at an angle of ?=69.0 with respect to the horizontal.…

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Q: A point charge q1 = +6.20 μC is held fixed at the origin. A second point charge with q2 = +1.50 μC…

A: Given,2 q1= +6.20μC (fixed at origin)  q2= +1.50μC ( at a distance +25cm from origin on x axis)…

Q: At the instant shown, car A is travelling along a straight road at a speed of 19 m/s while car B is…

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Q: A pendulum's angular position is given by ?= 0.0340 cos (?t), where ? is in radians and ? = 6.23…

A: Given, Angular position of a pendulum is  θ= 0.340cosωt  ω= 6.23 rad /sec

Q: A 120 g grapefruit is dropped from a tall building. What is the magnitude of its momentum after 2.00…

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Q: Oppositely charged parallel plates are separated by 4.97 mm. A potential difference of 600 V exists…

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Q: At what distance is the electrostatic force between two electrons equal to the weight of one?

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Q: A train is moving parallel and adjacent to a highway with a constant speed of 34 m/s. A car is…

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Q: | An RLC series circuit has R = 4 №, Xc = 3 №, and X₁ = 6 N. What is the impedance of this circuit?…

A: Given data:  An RLC circuit  R =  4 Ω Xc = 3 Ω and XL = 6 Ω Required: The impedance of this circuit

Q: (Treat as a kinematics problem) You are on a team that designs driver assist software for next…

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Q: Find the component form of v given its magnitude and the angle it makes with the positive x-axis.…

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Q: The figure shows a stream of water flowing through a hole at depth h = 4.50 cm in a tank holding…

A: Depth of hole h = 4.50 cm Height of water holding tank H = 31.4 cm To determine The distance ''x''…

Q: A 215-KV power transmission line carrying 500 A is hung from grounded metal towers by ceramic…

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Q: What is the speed of a 624 g basketball that has momentum with magnitude 5.85 kg.m/s?

A: We know thatP=mvv=PmWherev=speed of objectp=momentum of objectm=mass of object

Q: In the sport of billiards, event organizers often remove one of the rails on a pool table to allow…

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Q: A 170-g billiard ball is shot toward an identical ball at velocity vi = 7.70i m/s. The identical…

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Q: how many octaves are there between 27.5 Hz and 440 Hz? show how you arrived at your answer.

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Q: A cabinet of mass 8.8 kg is at rest on a ramp as shown. What is the magnitude of the normal force on…

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Q: Suppose the speed of sound in a certain location is 342 m/s. What is the temperature that…

A: Sound - Sound is a type of energy made by vibrations. When an object vibrates, it causes movement in…

Q: A 180-kg load is hung on a wire of length of 4.50 m, cross-sectional area 2.000 x 10-5 m2, and…

A: Given data:  Mass (m) = 180 kg Length (L) = 4.50 m Cross sectional area (A) = 2.000×10-5 m2 Young…

Q: A 7400 kg truck traveling along a straight road at 14 m/s comes to a stop and remains stationary for…

A: given         mass of truck (M )= 7400 kg        initial speed of truck (u) = 14 m/s        final…

Q: Sketch the vectors. Calculate for the resultant vector. Induce a methodical approach to the way of…

A: Visualize the Problem:

Q: E An aluminum block of mass my 4,05 kg and a copper block of mass m₂ 7.35 kg are connected by a…

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Q: Two objects attract each other with a gravitational force of magnitude 9.60 x 109 N when separated…

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Q: A crazy, young boy on a sled is able to get up to an incredible speed of 22.5 m/s (yes, he is…

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Q: Gold-197 has an atomic number of 79 and an atomic mass number of 197.  The mass of a gold nucleus…

A: Gold-197 has an atomic number of 79 and an atomic mass number of 197.    The mass of a gold nucleus…

Q: Set up the free-body diagram and equations for Newton's 2nd law for each object along each axis.…

A: Given,

Angular speed, acceleration and displacement

Angular acceleration is defined as the rate of change in angular velocity with respect to time. It has both magnitude and direction. So, it is a vector quantity.

Angular Position

Before diving into angular position, one should understand the basics of position and its importance along with usage in day-to-day life. When one talks of position, it’s always relative with respect to some other object. For example, position of earth with respect to sun, position of school with respect to house, etc. Angular position is the rotational analogue of linear position.