1. An object with the tregðustund of 2 kg m2 rotates at 1 rad/s. Hvað er angular momentum of the object?
Þekkt:
Tregðustund (I) = 2 kg m2
Angular speed (ω) = 1 rad/s
Óskað eftir: Skörpum skriðþunga (L)
Lausn:
Formula of angular momentum :
L = Ég ω
L= angular momentum (kg m2/s), I = tregðustund (kg m2), ω = hornhraði (rad/s)
The angular momentum :
L = Ég ω = (2)(1) = 2 kg/m²2/s
2. 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 ?
Þekkt:
Massi of pulley (M) = 2 kg
Radius of pulley (r) = 0.1 m
Angular speed (ω) = 2 rad/s
Óskað eftir: Skörpum skriðþunga
Lausn:
Formula of moment of inertia for solid cylinder :
I = 1/2 m r2
I = tregðustund (kg m2), m = massi (kg), r = radíus (M)
Moment of inertia :
I = 1/2 (2)(0.1)2 = (1)(0.01) = 0.01 kg/m2
The angular speed :
L = Ég 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.
Þekkt:
Massi af bolta (M) = 2 kg
Radius of ball (r) = 0.2 m
Angular speed (ω) = 4 rad/s
Óskað eftir: Skörpum skriðþunga
Lausn:
Formula of moment of inertia for uniform sphere :
I = (2/5) m r2
I = moment of inertia (kg m2), m = mass (kg), r = radíus (M)
The moment of inertia for uniform sphere :
I = (2/5)(2)(0.2)2 = (4/5)(0.04) = 0.032 kg m2
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.
Þekkt:
Massi of object (M) = 1 kg
The radius of circle (r) = 10 cm = 10/100 = 0.1 m
Hornhraðinn (ω) = 2 rad/s
Óskað eftir: Skörpum skriðþunga
Lausn:
Formula of moment of inertia for particle :
I = Hr.2 = (1)(0.1)2 = (1)(0.01) = 0.01 kg/m2
Angular momentum :
L = I ω = (0.01)(2) = 0.02 kg m2/s
