8 ROTATIONAL MOTION 8.9 Translational motion versus rotational motioņ ̧(^)
τ ≡ r × f = I α
Work W = f·dr Work W = τ·dφ
Power P = f·v Power P = τ·ω
Kinetic energy K = M v^2 /2 Kinetic energy K = I ω^2 /2
Table 3: The analogies between translational and rotational motion.
Likewise, the net work performed by the torque in twisting the body upon which
it acts through an angle ∆φ is just
W = τ ∆φ. (8.74)
8.9 Translational motion versus rotational motion
It should be clear, by now, that there is a strong analogy between rotational mo-
tion and standard translational motion. Indeed, each physical concept used to
analyze rotational motion has its translational concomitant. Likewise, every law
of physics governing rotational motion has a translational equivalent. The analo-
gies between rotational and translational motion are summarized in Table 3.
8.10 The physics of baseball
For that section I consulted G.R.Fowles „ Analytical Mechanics ”
Baseball players know from experience that there is a “sweet spot” on a baseball
bat, about 17 cm from the end of the barrel, where the shock of impact with the
ball, as felt by the hands, is minimized. In fact, if the ball strikes the bat exactly
on the “sweet spot” then the hitter is almost unaware of the collision. Conversely,
if the ball strikes the bat well away from the “sweet spot” then the impact is felt
as a painful jarring of the hands.
Translational motion Rotational motion
Displacement dr Angular displacement dφ
Velocity v = dr/dt Angular velocity ω = dφ/dt
Acceleration a = dv/dt Angular acceleration α = dω/dt
Mass
Force
M
f = M a
Moment of inertia
Torque
I = ̧^ ρ|ω^^ ×r|^2 dV