Math Is Fun Forum

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,384

Mechanics

Linear displacement

1) v = u + at

2) s = ut + ½at²

3) v² = u² + 2as

where u = initial velocity (Unit = meters/second)

v = final velocity (Unit = meters/second)

t = time (Unit = second)

a = acceleration (Unit = meters/second²)

s = displacement (Unit = meters)

Newton's second law of motion

F = ma

where F = Force (Unit=Newtons or kilograms meters/second²)

m = mass (Unit = kilograms)

a = acceleration (Unit = meters/second²)

w=mg

where w=weight (Unit kilograms meters/second²)

m=mass (Unit kilograms)

g=acceleration due to gravity (Unit meters/second²)

F = (G m1m2)/r²

where F = Force, G = Universal Gravitational Constant (Unit Newtons kilograms²/meters²)

r = distance between centers (Unit Meters)

p=mv

where p = momentum (Unit kilograms meters/second)

m = mass

v = velocity

Angular displacement

Torque = Moment of Inertia x radius x angular displacement

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: Mechanics

Angular Kinematics

Tangentenial Velocity = Angular Velocity × Radius   (m/s = (rad/s)×m)

Centripetal Acceleration = Tangentenial Velocity² / Radius   (m/s² = (m²/s²)/m)

Centripetal Acceleration = Angular Velocity² * Radius   ((rad²/s²)×m = m/s²)

Energy

Gravitational Potential Energy (gpe) = mgh (m = Mass (Kg), g = acceleration due to gravity (m/s²), h = height (m))

Linear Kinetic Energy (ke) = ½mv² (m = Mass (Kg), v = Velocity (m/s))

Rotational Kinetic Energy (ke) = ½Iw² (I = Moment of Inertia (Kgm²), w = rotational velocity (rad/s))

Elastic Potential Energy = Ex²/2l (E = Elastic Modulus/Young's Modulus (Pa), x = extension (m), l = original length (m))

Elastic Potential Energy = ½kx² (k = Spring Constant (Hooke's Law N/m), x = extension (m))

Elastic Potential Energy = ½fx (f = Force applied (N), x = extension (m))

Last edited by luca-deltodesco (2007-12-09 23:44:59)

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Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,384

Re: Mechanics

W=FS
where W is work done (in joules), F is force (in Newtons) and S is Displacement (in meters).

E=mc²
where E is Energy in Joules, m is mass in kilograms and c is velocity of light in meters per second (2.997x10^8)

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Re: Mechanics

I = m(v-u)
where I is impulse in Newton seconds, m is mass in kilograms, v is final velocty in metres per second and u is initial velocity in metres per second.

Moment = (magnitude of force) x (perpendicular distance from line of action of force to pivot)
Moment is measured in Newton metres, force in Newtons, and distance in metres.

Conservation of momentum:

where m is mass in kilograms, u is initial velocity in metres per second, and v is final velocity in metres per second
i.e. momentum before collision = momentum after collision (providing no external forces act)

F = μR
where F is maximum friction measured in Newtons, μ is the coefficient of friction between the two surfaces, and R is the normal contact force

Last edited by Daniel123 (2007-12-21 03:46:12)

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,384

Re: Mechanics

P=W/t where P is power in watts, W is work done in Joules, t is time in seconds.

E=mc²

where E is Energy in Joules, m is mass in kilograms, c is the velocity of light in meters per second.

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.