1. An object has the harakatsizlik momenti of 1 kg m2 rotates at a constant angular speed of 2 rad/s. Nima rotational kinetic energy of the object?
Ma'lum:
The moment of inertia (I) = 1 kg m2
The burchak tezligi (ω) = 2 rad/s
Kerakli: The rotational kinetic energy (KE)
yechim:
The formula of the rotational kinetic energy :
KE = 1/2 I ω2
KE = the rotational kinetic energy (kg/m2/s2), I = the moment of inertia (kg/m2), ω = burchak tezligi (rad/s)
The rotational kinetic energy :
KE = 1/2 I ω2 = 1/2 (1)(2)2 = 1/2 (1)(4) = 2 Joul
2. 20 kg vaznli cylinder pulley with a radius of 0.2 m rotates at a constant angular speed of 4 rad/s. What is the rotational kinetic energy of the pulley?
Ma'lum:
Mass of cylinder pulley (m) = 20 kg
The radius of cylinder (r) = 0.2 m
Burchak tezligi (ω) = 4 rad/s
Qidirilgan: What is the rotational kinetic energy
Solution ;
Formula of the moment inertia of cylinder :
I = 1/2 m r2
I = the moment of inertia (kg m2), m = mass (kg), r = radiusi (meter)
Silindr kasnagining inersiya momenti:
I = 1/2 (20)(0.2)2 = (10)(0.04) = 0.4 kg m2
The rotational kinetic energy of the pulley :
KE = 1/2 I ω2 = 1/2 (0.4)(4)2 = (0.2)(16) = 3.2 Joul
3. A-10 kg ball with radius of 0.1 m rotates at a constant of 10 rad/s. What is the kinetic energy of the ball.
Ma'lum:
Mass to'pning (m) = 10 kg
Radius of ball (r) = 0.1 m
Burchak tezligi (ω) = 10 rad/s
Qidirilgan: The rotational kinetic energy
yechim:
Formula of the moment of inertia :
I = (2/5) m r2
I = harakatsizlik momenti (kg/m2), m = mass (kg), r = radiusi (m)
Moment of inertia of the ball :
I = (2/5)(10)(0.1)2 = (4)(0.01) = 0.04 kg m2
The rotational kinetic energy of the ball :
KE = 1/2 I ω2 = 1/2 (0.04)(10)2 = (0.02)(100) = 2 Joul
4. A 0.5-kg particle rotates at a constant angular speed of 2 rad/s. What is the rotational kinetic energy of the particle if the radius of circle is 10 sm.
Ma'lum:
Mass of particle (m) = 0.5 kg
The radius of ball (r) = 10 cm = 10/100 = 0.1 m
Burchak tezligi (ω) = 2 rad/s
Qidirilgan: The rotational kinetic energy
yechim:
Moment of inertia for particle :
I = Janob2 = (0.5)(0.1)2 = (0.5)(0.01) = 0.005 kg m2
The rotational kinetic energy :
KE = 1/2 I ω2 = 1/2 (0.005)(2)2 = 1/2 (0.005)(4) = (0.005)(2) = 0.01 Joul
