Chapter 8. Magnitude of the angular momentum of particle (8-23)

Question

kvPTqi/0KpnMV5+TH/Df+Aa5ntcMP8zrGgU0VcJNmx7YsiGGhhyT/mpbCUG99fNmphLDyg==
{"title":"Magnitude of the angular momentum of a particle","description":"Correct!","type":"correct","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"1,2,32,42\"}]"} {"title":"Component of the particle’s linear momentum perpendicular to the vector r from rotation axis to particle","description":"Wrong","type":"incorrect","color":"#ffcc00","code":"[{\"shape\":\"rect\",\"coords\":\"118,11,119,13\"},{\"shape\":\"rect\",\"coords\":\"88,12,113,46\"},{\"shape\":\"rect\",\"coords\":\"154,37,157,37\"},{\"shape\":\"rect\",\"coords\":\"222,8,271,42\"}]"} {"title":"istance from the rotation axis to the particle","description":"Incorrect","type":"incorrect","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"171,12,190,38\"},{\"shape\":\"rect\",\"coords\":\"69,14,88,39\"}]"}

Question

5RBDhATNYZKM9J82m+ad57g3GWtwr1cWoCbIvqyslE9mjGS6+caUtaI/4UPHigbxFKPynEpL/0EqyVv78nMPLZ5SOu82irGA7WYJLzz50c05H8aqKmwO/K/uBzqQZcYibCRESWUtY03+i2WbGioKXA==
{"title":"Magnitude of the angular momentum of a particle","description":"Wrong","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"1,2,32,42\"}]"} {"title":"Component of the particle’s linear momentum perpendicular to the vector r from rotation axis to particle","description":"Correct!","type":"correct","color":"#ffcc00","code":"[{\"shape\":\"rect\",\"coords\":\"118,11,119,13\"},{\"shape\":\"rect\",\"coords\":\"88,12,113,46\"},{\"shape\":\"rect\",\"coords\":\"154,37,157,37\"},{\"shape\":\"rect\",\"coords\":\"222,8,271,42\"}]"} {"title":"Distance from the rotation axis to the particle","description":"Incorrect","type":"incorrect","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"171,12,190,38\"},{\"shape\":\"rect\",\"coords\":\"69,14,88,39\"}]"}

Question

WYeoCoimm3bicL5RPBUcZJg+DDK8luGwIWfsChfUEGyoJlv8YaI1kjIWeGpb5G3AprmU7A==
{"title":"Magnitude of the angular momentum of a particle","description":"Wrong","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"1,2,32,42\"}]"} {"title":"Component of the particle’s linear momentum perpendicular to the vector r from rotation axis to particle","description":"Incorrect","type":"incorrect","color":"#ffcc00","code":"[{\"shape\":\"rect\",\"coords\":\"118,11,119,13\"},{\"shape\":\"rect\",\"coords\":\"88,12,113,46\"},{\"shape\":\"rect\",\"coords\":\"154,37,157,37\"},{\"shape\":\"rect\",\"coords\":\"222,8,271,42\"}]"} {"title":"Distance from the rotation axis to the particle","description":"Correct!","type":"correct","color":"#333300","code":"[{\"shape\":\"rect\",\"coords\":\"171,12,190,38\"},{\"shape\":\"rect\",\"coords\":\"69,14,88,39\"}]"}

Review

Figure 8-27 shows that only the component of the momentum \(\vec{p}\) that’s perpendicular to \(\vec{r}\) contributes to rotation around the axis, so only this component \(p_\perp = p \sin{\theta}\) contributes to the angular momentum. We define the magnitude of the angular momentum as: