Unizor - Physics4Teens - Mechanics - Rotational Dynamics - Problems скачать в хорошем качестве

Unizor - Physics4Teens - Mechanics - Rotational Dynamics - Problems

Unizor - Physics through a Looking Glass of Mathematician Problems on Rotational Dynamics Problem 1 Consider a device that consists of a wheel of radius r and mass M, freely rotating on some fixed axis, a thread rolled around it a few times and a point-object of mass m hanging off that thread. Assume that all mass of a wheel is concentrated in its rim, while spokes are weightless. There is no friction in the rotating wheel. A thread is weightless and unstrechable. The force of gravity pulls the object down with free fall acceleration g. What will be the acceleration of an object? Problem 2 Calculate a moment of inertia of disk of mass M and radius R rotating around an axis going through its center perpendicularly to its surface. Problem 3 Consider Problem 1, but change a wheel with all mass concentrated in the rim with a wheel with mass evenly distributed inside the circumference, making it a disk. Problem 4 Let's rotate a small ball of mass M within a horizontal plane on a thread of length D. The thread will make certain angle φ with the horizon. Experiments show that the angle will be smaller if a ball rotates faster. Determine the relationship between angular speed of rotation ω, mass of a ball M, length of a thread D and angle φ, ignoring friction and air resistance.