Find the length of a rope: Rope unwounded from a cylindrical wheel
Question: A cylindrical wheel with radius of 2-m rotates on a fixed frictionless horizontal axis. The moment of inertia of […]
Find the current as a function of time: A Resistor-inductor circuit with a steady voltage source
Question: A circuit that has a resistor, \(R\), and an inductor, \(L\), which are connected in series with a DC […]
Finding the magnetic field with Ampere’s law: A toroid carrying current
Question: A toroid has \(N\) turns both sides carrying equal current \(I\). The inner and outer radii are \(a\) and […]
Finding the enclosed area between a parabola and a circle
Question: A parabola is given as \[ y=\frac{1}{4}x^2-1 \] A circle is also given in the same plane: \[ x^2+y^2=16 […]
How to add velocities in terms of the special theory of relativity
Question: The speed of light is measured in a liquid that has refractive index of \(n\). If the liquid is […]
Finding the electric potential of a thin finite rod
Question: A thin rod is placed along the z-axis that is stretched from \(z=-d\) to \(z=+d\). Let \(\lambda\) be the […]
Infinite integral of the exponential and trigonometric function
Question: Find the value of the following integral: \[ \int^{\infty}_{-\infty}e^{-x^2}\cos 2bxdx \] Answer: Let \[ \int^{\infty}_{-\infty}f(x,b)dx = 2\int^{\infty}_{0}f(x,b)dx \] where […]
Finding the magnetic field from the electric field: EM waves
Question: The electric field of an electromagnetic wave is given as \[ \vec{E}=(E_{0x}\vec{x} + E_{0y}\vec{y})\sin(\omega t – kz + \phi) […]
The free-fall human and its kinematics
Question: A stunt woman jumps off from a 202-m high building onto a cushion having a thickness of 2.00 m. […]
Invariance of physics under Galilean transformation
Question: Physics laws cannot be altered by the observer’s frames of reference. The transformation from a lab reference frame to […]