1. An object with the inercijos momentas of 2 kg m2 rotates at 1 rad/s. Kas yra kampinis pagreitis of the object?
Žinomas:
Inercijos momentas (I) = 2 kg m2
Kampinis greitis (ω) = 1 rad / s
Ieškoma: Kampinis pagreitis (L)
sprendimas:
Formula of angular momentum :
L = I ω
L = kampinis pagreitis (kg m²)2/s), I = inercijos momentas (kg m²)2), ω = kampinis greitis (rad/s)
Kampinis momentas:
L = I ω = (2)(1) = 2 kg m2/s
2. 2 XNUMX-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 ?
Žinomas:
Masė of pulley (M) = 2 tūkstg
Radius of pulley (r) = 0.1 m
Kampinis greitis (ω) = 2 rad/s
Ieškoma: Kampinis pagreitis
sprendimas:
Formula of moment of inertia for solid cylinder :
I = 1/2 m r2
I = inercijos momentas (kg m²)2), m = masė (kilogramas), r = spindulys (M)
Inercijos momentas:
I = 1/2 (2)(0.1)2 = (1)(0.01) = 0.01 kg m2
The angular speed :
L = I ω = (0.01)(2) = 0.02 kg m2/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.
Žinomas:
Masė of ball (M) = 2 kg
Radius of ball (r) = 0.2 m
Kampinis greitis (ω) = 4 rad/s
Ieškoma: Kampinis pagreitis
sprendimas:
Formula of moment of inertia for uniform sphere :
I = (2/5) m r2
I = moment of inertia (kg m²)2), m = mass (kg), r = spindulys (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 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.
Žinomas:
Masė of object (M) = 1 tūkstg
The radius of circle (r) = 10 cm = 10/100 = 0.1 m
The angular speed (ω) = 2 rad/s
Ieškoma: Kampinis pagreitis
sprendimas:
Formula of moment of inertia for particle :
I = m r2 = (1)(0.1)2 = (1)(0.01) = 0.01 kg m2
Angular momentum :
L = I ω = (0.01)(2) = 0.02 kg m2/s
