Classical Mechanics

Projectile Motion – Fired at ground level
A football is kicked with an initial velocity of 25 m/s at an angle of 45-degrees with the horizontal. Determine the time of flight, the horizontal displacement, and the peak height of the football .....

Projectile Motion – Pool ball leaves the table with initial horizontal velocity
A pool ball leaves a 0.20-meter high table with an initial horizontal velocity of 2.4 m/s. Predict the time required for the pool ball to fall to the ground and the horizontal distance between the tab...

Force on a batted ball – Impulse
A baseball (m = 0.14 kg) thrown by a pitcher reaches a bat with a velocity of 32.0 m/s in a horizontal direction. a) Computer the impulse that must be applied to the ball if it is to leave the...

Average impact force between and airliner and a bird
Estimate the average impact force between an airliner traveling at 260 m/s and with a 0.3 kg bird whose length is 20 cm?The change in velocity of the bird is estimated to be 260 m/s Thes...

Find Earth angular momentum
Find Earth angular momentum using Earth-Sun distance and mass of Earth? Earth - Sun distance 149.6x109 m Mass of the Earth 5.9742x1024 kgEarth angular momentumFor an orbit, angular momen...

Find speed of a satellite placed at geostationary orbit
A 270 kg communication satellite is placed in a geostationary orbit 35,780 km above a relay Earth ground level. What is the speed of the satellite in orbit? A geostationary o...

Find moment of inertia of a uniform hollow cylinder
We know that the moment of inertia for hoop with radius R is mR2. We can divide cylinder into thin concentric hoops of thickness dR. Deity = Mass per unit volume Deity...

Kinetic energy for single particle with constant mass
Show that for a single particle with cotant mass the equation of motionimplies the following differential equation for the kinetic energy:while if the mass varies with time the corresponding equa...

Prove that position vector for the center of mass from an arbitrary origin is given by this equation
Prove that the magnitude R of the position vector for the center of mass froman arbitrary origin is given by the equation:(Source: Herbert Goldstein, Classical Mechanics - Chapter 01)...

Lagrange for uniform thin disk
Coider a uniform thin disk that rolls without slipping on a horizontal plane. A horizontal force is applied to the center of the disk and in a direction parallel to the plane of the disk.De...

Escape veolcity for Earth
The escape velocity of a particle on Earth is the minimum velocity required at Earth's surface in order that that particle can escape from Earth's gravitational field. Neglecting the resistance of the...

Equation of motion for a rocket
Rockets are propelled by the momentum reaction of the exhaust gases expelled from the tail. Since these gases arise from the raction of the fuels carried in the rocket, the mass of the rocket is no...

Points of mass joined by rigid rod
Two points of mass m are joined by a rigid weightless rod of length l, the center of which is cotrained to move on a circle of radius a. Express the kinetic energy in generalized coordinates. (S...