Classical Mechanics (Kibble & Berkshire) · Problem 11.6

Lagrange's equations and conservation principles — T.W.B. Kibble, F.H. Berkshire

Physics — Mechanics · baseball-bat-impact

Problem

Baseball bat A baseball bat has mass

M

and moment of inertia

Mk^2

about any axis through its centre of mass

G

that is perpendicular to the axis of symmetry. The bat is at rest when a ball of mass

m

, moving with speed

u

, is normally incident along a straight line through the axis of symmetry at a distance

b

from

G

. Show that, whether the impact is elastic or not, there is a point on the axis of symmetry of the bat that is instantaneously at rest after the impact and that the distance

c

of this point from

G

is given by

bc = k^2

. In the elastic case, find the speed of the ball after the impact. [Gravity (and the batter!) should be ignored throughout this question.]

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