1. An object with the mumentu di inertzia of chilò 2 m2 rotates at 1 rad/s. Chì hè u impetu angulare of the object?
Cunnisciutu:
Mumentu di inertzia (I) = 2 kg m2
A velocità angulare (ω) = 1 rad/s
Cercatu: Momentu angulare (L)
Soluzione:
Formula of angular momentum :
L = Eiu ω
L= impetu angulare (kg m²)2/s), I = mumentu di inertzia (kg m²)2), ω = angular speed (rad/s)
The angular momentum :
L = Eiu ω = (2)(1) = 2 kg m2/s
2. A 2-kg cylinder pulley with radius of 0.1 m francese rotates at a constant angular speed of 2 rad/s. What is the angular momentum of the pulley ?
Cunnisciutu:
Missa of pulley (m) = 2 kg
Radius of pulley (r) = 0.1 m
A velocità angulare (ω) = 2 rad/s
Cercatu: Momentu angulare
Soluzione:
Formula of moment of inertia for solid cylinder :
I = 1/2 m r2
I = mumentu di inertzia (kg m²)2), m = di massa (kg), r = raiu (m)
Mumentu d'inerzia:
I = 1/2 (2)(0.1)2 = (1)(0.01) = 0.01 kg m²2
The angular speed :
L = Eiu ω = (0.01)(2) = 0.02 kg m2/s
3. A 2-kg uniform sphere with radius of 0.2 m francese rotates at 4 rad/s. What is the angular momentum of the ball.
Cunnisciutu:
Missa of ball (m) = 2 kg
Radius of ball (r) = 0.2 m
A velocità angulare (ω) = 4 rad/s
Cercatu: Momentu angulare
Soluzione:
Formula of moment of inertia for uniform sphere :
I = (2/5) m r2
I = moment of inertia (kg m²)2), m = mass (kg), r = raiu (m)
The moment of inertia for uniform sphere :
I = (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 m2/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.
Cunnisciutu:
Missa of object (m) = 1 kg
The radius of circle (r) = 10 cm = 10/100 = 0.1 m
A velocità angulare (ω) = 2 rad/s
Cercatu: Momentu angulare
Soluzione:
Formula of moment of inertia for particle :
I = Sr.2 = (1)(0.1)2 = (1)(0.01) = 0.01 kg m²2
Angular momentum :
L = I ω = (0.01)(2) = 0.02 kg m2/s
