A rigid stick is pivoted at the origin and is arranged to swing around in a...

A rigid stick is pivoted at the origin and is arranged to swing around in a horizontal plane at a constant angular speed omega. A bead of mass m slides frictionlessly along the stick. Let r be the radial position of the bead. Find the Hamiltonian. Is it conserved? Explain why this quantity is not the energy of the bead.

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genius_generous answered 2 years ago

Three spherical surface charges σ1, σ2 and σ3 are arranged concentrically around the origin of a...

Three spherical surface charges σ1, σ2 and σ3 are arranged concentrically around the origin of a Cartesian coordinate system with the radii r1, r2 and r3. It applies σ1=(-2Q)/(4πr1^2), σ2=(+2Q)/(4πr2^2) and σ3=(-2Q)/(4πr3^2), where Q >0 describes an initially unknown amount of charge. Furthermore, the following applies in the entire room: ε=ε0 A point charge with the charge +Q is located at a point with the distance R to the origin. R > r3 applies. Determine the force F, which acts...

A meter stick on a horizontal frictionless table top is pivoted at the 80-cm mark. A...

A meter stick on a horizontal frictionless table top is pivoted at the 80-cm mark. A force F1 = 5 N is applied perpendicularly to the end of the stick at 0 cm, as shown. A second force F2 (not shown) is applied at the 100-cm end of the stick. The stick does not rotate. a) What is the torque (magnitude and sign) about the pivot from F1? b) Explain why the torque from the pivot about itself is zero....

A uniform stick 1.3 m long with a total mass of 270 g is pivoted at...

A uniform stick 1.3 m long with a total mass of 270 g is pivoted at its center. A 3.8-g bullet is shot through the stick midway between the pivot and one end. The bullet approaches at 250 m/s and leaves at 140 m/s. With what angular speed is the stick spinning after the collision?

A particle of mass m orbits around the origin (0,0) in a circular path of radius...

A particle of mass m orbits around the origin (0,0) in a circular path of radius r. (a) Write the classical Hamiltonian (energy) of this system in terms of angular momentum of the particle. (b) Write the Schrodinger equation for this system. (c) Find the energy eigenvalues and their corresponding (normalized) wavefunctions.

8. A rigid object with moment of inertia 25 Kg m^2 is spinning around a fixed...

8. A rigid object with moment of inertia 25 Kg m^2 is spinning around a fixed axis with angular speed of 10 rad/s. A constant torque of 50 Nm is applied in a direction that slows down the rotation, for 2 seconds. (i) Calculate the angular speed of the object at t = 5 s. (ii) Calculate the kinetic energy of the object at t = 5 s. 9.A disc of moment of inertia 10 kg m^2 about its center...

How do you do a 90 degree counter-clockwise rotation around a point? I know around the origin it's (−y,x), but what would it be around a point?

f(x,y)=(xcos(t)−ysin(t),xsin(t)+ycos(t))f(x,y)=(xcos⁡(t)−ysin⁡(t),xsin⁡(t)+ycos⁡(t)) defines rotation around the origin through angle tt in the Cartesian plane R2R2. If one...

f(x,y)=(xcos(t)−ysin(t),xsin(t)+ycos(t))f(x,y)=(xcos⁡(t)−ysin⁡(t),xsin⁡(t)+ycos⁡(t)) defines rotation around the origin through angle tt in the Cartesian plane R2R2. If one rotates a point (x,y)∈R2(x,y)∈R2 around the origin through angle tt, then f(x,y)f(x,y) is the result. Let (a,b)∈R2(a,b)∈R2 be an arbitrary point. Find a formula for the function gg that rotates each point (x,y)(x,y) around the point (a,b)(a,b) through angle tt.

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