1. An object with the àm inertia of 2 kg m2 rotates at 1 rad/s. Dè tha a ' gluasad ceàrnach den nì?
Aithnichte:
Mionaid inertia (I) = 2 kg m2
Angular speed (ω) = 1 rad/s
A dhìth: Angular momentum (L)
fuasgladh:
Formula of angular momentum :
L = Mise ω
L= gluasad ceàrnach (kg m2/s), I = àm inertia (kg m2), ω = astar ceàrnach (rad/s)
The angular momentum :
L = Mise ω = (2)(1) = 2 kg m2/s
2. Tha 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 ?
Aithnichte:
Aifreann of pulley (m) = 2 mìleg
Radius of pulley (r) = 0.1 m
Angular speed (ω) = 2 rad/s
A dhìth: Angular momentum
fuasgladh:
Formula of moment of inertia for solid cylinder :
I = 1/2 m r2
Mise = àm inertia (kg m2), m = tomad (kg), r = radius (m)
Mionaid neo-sheasmhachd:
I = 1/2 (2)(0.1)2 = (1)(0.01) = 0.01 kg m2
The angular speed :
L = Mise 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.
Aithnichte:
Aifreann of ball (m) = 2 kg
Radius of ball (r) = 0.2 m
Angular speed (ω) = 4 rad/s
A dhìth: Angular momentum
fuasgladh:
Formula of moment of inertia for uniform sphere :
I = (2/5) m r2
I = moment of inertia (kg m2), m = mass (kg), r = radius (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.
Aithnichte:
Aifreann of object (m) = 1 mìleg
The radius of circle (r) = 10 cm = 10/100 = 0.1 m
An astar ceàrnach (ω) = 2 rad/s
A dhìth: Angular momentum
fuasgladh:
Formula of moment of inertia for particle :
I = Mgr.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
