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2” 6”

1”

8”

8”

F

1”

F

The disk and shaft shown are rotated at 2000 rpm, and there is an angular acceleration

of 20 rev/(sec.sec.). The steel part is held in a cantilevered bearing that can be approximated

with the forces shown.

12.3.3 Impulses and Momentum

• Momentum is a convenient alternative to energy in analysis of systems.

12.3.3.1 - Linear Momentum

• momentum is defined as,

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t2 t2

∫ F( t) dt = ∫ mA( t) dt = mV( t2) – mV( t1) = L( t)

t1	t1
	Impulse	Momentum

•If no external forces are applied, momentum remains constant (is conserved). In this case L is a constant.

•An impulse is a force applied that will change momentum.

12.3.3.2 - Angular Momentum

•Angular momentum is for rotating objects. The rotation about some center tends to make these equations a bit more complicated than linear momentum.

•We can start to find this as a velocity times a distance of rotation, and this will lead to the eventual relationships,

∑

∑

∑

MMx	= IMxx α x – IMxy α y – IMxz α z + ω yHz – ω zHy
MMy	= –IMyx α x + IMyy α	y – IMyz α z + ω zHx – ω x Hz
MMz	= –IMxzx α x – IMzy α	y + IMzz α z + ω xHy – ω yHx

• These equations show the angular momentum H, along with other familiar terms.