1. An object with the lub sij hawm ntawm inertia of 2 kg m2 rotates at 1 rad/s. Yuav ua li cas yog lub lub zog ntawm lub kaum sab xis ntawm tus khoom?
Paub:
Lub sijhawm ntawm inertia (Kuv) = 2 kg m2
Qhov ceev ntawm lub kaum sab xis (ω) = 1 rad/s
Xav tau: Angular zog (L)
Tshuaj:
Formula of angular momentum :
L = Kuv ω
L = tau lub zog ntawm lub kaum sab xis (kg/m²)2/s), I = lub sij hawm ntawm inertia (kg/m²)2), ω = qhov ceev ntawm lub kaum sab xis (rad/s)
The angular momentum :
L = Kuv ω = (2)(1) = 2 kg/m²2/s
2. A 2-kg cylinder pulley with radius of 0.1 m rotates at a constant angular speed of 2 rad/s. What is the angular momentum of the pulley ?
Paub:
Pawg of pulley (M) = 2 kg
Radius of pulley (r) = 0.1 m
Qhov ceev ntawm lub kaum sab xis (ω) = 2 rkev tshaj tawm
Xav tau: Angular zog
Tshuaj:
Formula of moment of inertia for solid cylinder :
I = 1/2 mr2
Kuv = lub sij hawm ntawm inertia (kg/m²)2), m = loj (kg), r = vojvoog (M)
Lub sijhawm ntawm inertia:
Kuv = 1/2 (2)(0.1)2 = (1)(0.01) = 0.01 kg m²2
The angular speed :
L = Kuv ω = (0.01)(2) = 0.02 kg/m²2/s
3. A 2-kg uniform sphere with radius of 0.2 m rotates at 4 rad/s. What is the angular momentum of the ball.
Paub:
Pawg ntawm lub pob (M) = 2 kg
Radius ntawm lub pob (r) = 0.2 m
Qhov ceev ntawm lub kaum sab xis (ω) = 4 rahnub/s
Xav tau: Angular zog
Tshuaj:
Formula of moment of inertia for uniform sphere :
I = (2/5) Yawg.2
I = moment of inertia (kg/m²)2), m = pawg (kg), r = vojvoog (M)
The moment of inertia for uniform sphere :
Kuv = (2/5)(2)(0.2)2 = (4/5)(0.04) = 0.032 kg m²2
The angular momentum of sphere :
L = I ω = (0.032)(4) = 0.128 kg/m²2/s
4. A 1-kg particle rotates at a constant angular speed of 2 rad/s. What is the angular speed if the radius of circle is 10 cm.
Paub:
Pawg of object (M) = 1 kg
The radius of circle (r) = 10 cm = 10/100 = 0.1 m
Qhov ceev ntawm lub kaum sab xis (ω) = 2 rad/s
Xav tau: Angular zog
Tshuaj:
Formula of moment of inertia for particle :
I = Yawg.2 = (1)(0.1)2 = (1)(0.01) = 0.01 kg m²2
Angular momentum :
L = Kuv ω = (0.01)(2) = 0.02 kg m2/s
