Rolling a cylindrical rigid object on an inclined plane
Question: A circular cylinder of radius \(r\) rolls down on an inclined plane from height \(h\). Compare the velocities at […]
Find the magnetic field due to the revolution of an electron: Hydrogen atom
Question: Use Bohr theory. Find the magnetic field due to electron’s revolution about the nucleus of the hydrogen atom. The […]
The rocket launch: Changing mass and its motion
Question: A rocket is launched in a constant gravity, 9.80 m/s\(^2\). The initial velocity is 400 m/s, and the burn […]
A projectile motion with air resistance that is proportional to its velocity
Question: A ball is thrown and it tracks a projectile near the Earth’s surface subject to a resistive force due […]
Find the natural frequency: Free ends of a spring connected with two objects
Question: Two objects which have equal masses, \(m\), are connected with a spring whose force constant is \(k\). The objects […]
Find the lifetime of Delta baryon with the uncertainty principle
Question: The Delta baryon, \(\Delta\), is known as the lowest nucleon resonance that has a mass of 1232 MeV/c\(^2\) and […]
How to calculate the time dilation due to a traveling airplane
Question: Physicists conduct an experiment to measure time dilation of an atomic clock in a flying airplane. If the velocity […]
How to solve the differential equation: \((x^2\cos x – y)dx + xdy = 0\)
Question: Solve \((x^2\cos x – y)dx + xdy = 0\). Answer: Rewrite the equation as follows: \[ \frac{dy}{dx}-\frac{y}{x}=-x\cos x \] […]
Solve the differential equation: \(x\frac{dy}{dx}+y=x\ln x\)
Question: (1) Solve \(x\frac{dy}{dx}+y=0\) (2) Solve \(x\frac{dy}{dx}+y=x\ln x\) by using the result from (1). Answer: (1) The original differential equation […]
Solve the differential equation, \(\frac{dy}{dx}+P(x)y=Q(x)\).
Question: (1) Find the general solution of \(\frac{dy}{dx}+P(x)y=Q(x)\), where \(P(x)\) and \(Q(x)\) are functions of \(x\). (2) Solve the following […]