Formulas for Physics 1A - University of California, San Diego

Formulas for Physics 1A

¦Á ¡Ô angular acceleration (1/s2)

F ¡Ô force (N ¡Ô kg?m/s2)

G ¡Ô gravitational constant = 6.67 x 10-11 m3/(kg?s3)

k ¡Ô spring constant (kg/s2)

? ¡Ô coefficient of friction

N ¡Ô normal force

P ¡Ô pressure (Pa ¡Ô kg/m?s2)

¦Ó ¡Ô torque (N?m ¡Ô kg?m2/s2)

¦È ¡Ô angular displacement or rotation

¦Ø ¡Ô angular velocity (1/s)

X ¡Ô displacement (m)

A ¡Ô acceleration (m/s2)

g ¡Ô gravitat. acceleration at Earths surface = 9.81 m/s2

I ¡Ô moment of inertia (kg/m2)

L = angular momentum (kg?m2/s)

m ¡Ô mass (kg)

P ¡Ô momentum (kg?m/s)

¦Ñ ¡Ô density (kg/m3)

T ¡Ô period of orbit

V ¡Ô velocity (m/s)

W ¡Ô work (J = N?m = kg?m2/s2)

Y ¡Ô displacement (m)

Kinematics

For A = Constant:

V(t) = V0 + A?t

and

X(t) = X0 + V0?t + (1/2)?A?t2

2

2

The above two equations lead to: V (t) = V 0(t) + 2?A?[X(t) ¨C X0]

Forces

F(t) = m(t)?A(t) (where we explicitly note that both mass and acceleration can change with time)

P(t) = m(t)?V(t) (where F = ¦¤P/¦¤t or ¦¤P = F¦¤t; the change in momentum ¦¤P is also referred to as impulse)

Friction models

fstatic friction ¡Ü ?s?N (opposes the direction of motion up to a maximum value of ?s?N)

fkinetic friction = ?k?N (opposes the direction of motion)

Rocket equation

V = ?exhaust?ln(Minitial/Mfinal)

Spring equation

F(t) = k?[x(t) ¨C x0]

Gravitational formula

F = (G?M1?M2)/R212 (points radially inward)

T2 = [(4¦Ð2)/(G?Msun)]?R3 (Kepler¡¯s third law, where T = 2¦Ð/¦Ø)

Rotational motion

For ¦Á = Constant

¦Ø(t) = ¦Ø0 + ¦Á?t

and

¦È(t) = ¦È0 + ¦Ø0?t + (1/2)?¦Á?t2

Atangent = R?¦Á

and

Vtangent(t) = R?¦Ø(t)

Acentrifugal(t) = R?¦Ø2(t) = V2tangent(t)/R (points radially inward)

¦Ó(t) = R?F(t)?sin¦È (where the angle extends from the radius vector to the force vector)

¦Ó(t) = I?¦Á(t)

L(t) = I?¦Ø(t) (where ¦Ó = ¦¤L/¦¤t)

I ¡Ô ¦²imiri2 = M?R2 (point mass); M?R2 (thin cylindrical shell); (2/3)?M?R2 (thin spherical shell); (1/2)?M?R2

(solid cylinder rotated on axis); (1/3)?M?L2 (rod rotated about end); (1/5)?M?R2 (solid sphere);

(1/12)?M?L2 (rod rotated about center); where R is the radius and L is the length

Work and Energy

W = F?(Xfinal ¨C Xinitial)?cos¦È (where the angle is between the force vector and the displacement vector)

Conservative forces: KE + PE = Constant

Nonconservative forces: KE + PE ¡Ù Constant

2

Translation: KE = (1/2)?m?V

Rotation: KE = (1/2)?I?¦Ø2

Gravitational: PE = - (G?M1?M2)/R12

Spring: PE = (1/2)?k?[X(t) ¨C X0]2

Fluids

Continuity: A?V = A¡¯?V¡¯

Bernouli: P + ¦Ñ?g?Y + (1/2)?¦Ñ?V2 = Constant

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