Angular Impulse–Momentum

\int_{t_{1}}^{t_{2}} M_{O} d t = H_{O 2} - H_{O 1} = I_{O} ω_{2} - I_{O} ω_{1}

Moment integrated over time changes angular momentum about a fixed point O or the mass center. Impacts with a known angular impulse (or a pin reaction with no moment) are the usual FE setup.

$M_{O}$ (N·m): Moment about O
$H_{O}$: Angular momentum Iω

Step-by-step solved example

Disk I=2 kg·m² at 10 rad/s is braked by 4 N·m. Time to stop?

∫M dt changes Iω of the shaft / disk.

1. Impulse
−4 Δt = 2(0−10).
2. Time
Δt=5 s.
$Δ t = 5 s$

Answer: 5 s

10 practice questions

0/10 correct

1.If M_O=0 then H_O is

2.Linear impulse Σ∫F dt equals

3.A pin at O does not change H_O because

4.I=5, ω from 4 to 10 rad/s, M=3: Δt =

5.Central impact of two particles conserves

6.Units of angular impulse are

7.For a particle, H_O =

8.Constant M gives constant

9.During a short impact, finite moments from gravity are often

10.H about G (mass center) is