RaP: Acceleration of point P in reference frame R (m/s2) aP = EaP: Acceleration of point P in the reference frame E, which is fixed on earth ac: Acceleration of the center of mass of a body in the inertial reference frame E
a: Angular acceleration of body B in reference frame E (1/s)
B: Represents a body with volume V and mass m bi, b2, b2: Orthogonal unit vectors associated with body B
C: Center of mass da/dt: Time derivative of a d2a/dt2: Second time derivative of a
E: Reference frame fixed on earth
E: Young's modulus for elastic materials (N/m2)
e: Strain, ratio of change in length to stress-free length of a line element e1, e2, e2: Orthogonal unit vectors defining the reference frame E F: Force (N)
fif Force exerted by mass element j on the mass element i within a body
B (system of particles) g: Gravitational acceleration (m/s2)
Hc: Moment of momentum of a body (system of particles) about a point C
H0: Moment of momentum of a body (system of particles) about a point O (kg-m2/s)
Icf ijth component of mass moment of inertia about the center of mass (kg-m2)
Pf ijth component of mass moment of inertia about point O Jx: Axial moment of inertia (m4) k: Spring constant (N/m) k: Radius of gyration (m) A: Angular impulse (N-m-s)
L: Linear momentum of a particle, body, or system of particles (kg-m/s) Mo: Moment of a force about point O (N-m)
m: Mass of a particle or a body (kg) /.i: Coefficient of friction
P: Mechanical power (rate of work done by a system of forces) (N-m/s) rP/O: Position vector connecting point O to point P (m) p: Position vector connecting the center of mass of a body to a point of the body a: Stress, force intensity, force per unit area (N/m2) t: Time
T: Tension in a cable, tendon, or ligament (N)
V: Potential energy (N-m)
V: Rate of shortening, ratio of rate of change of length to the length of a muscle fiber (1/s) RvP: Velocity of point P in reference frame R (m/s) vP = EvP: Velocity of point P in the reference frame E, which is fixed on earth
w: Load per unit area (length) that is acting on a structure (N/m2 or N/m) rmb: Angular velocity of rigid body B in reference frame R (1/s) m: Angular velocity of body B in reference frame E Ç: Impulse (N-s)
Notes: The terms in parentheses present the units of each variable. The abbreviations kg, m, N, and s stand, respectively, for kilogram, meter, Newton, and second. In general, a left superscript refers to a reference frame under consideration. For simplicity, we omit the superscript when the reference frame is one that is fixed on Earth. A right superscript may indicate a point or a body. Frequently, we omit this superscript when the text clearly indicates which point or body is being referred to. The subscripts typically indicate a component along a certain coordinate axis.
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The use of dumbbells gives you a much more comprehensive strengthening effect because the workout engages your stabilizer muscles, in addition to the muscle you may be pin-pointing. Without all of the belts and artificial stabilizers of a machine, you also engage your core muscles, which are your body's natural stabilizers.