1. An object has the 관성 모멘트 of 1 kg m2 rotates at a constant angular speed of 2 rad/s. 무엇인가 rotational kinetic energy of the object?
알려진 바에 따르면:
관성 모멘트 (I) = 1 kg m2
The 각속도 (ω) = 2rad / s
구함 : The rotational kinetic energy (KE)
솔루션 :
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 = 각속도 (rad/s)
The rotational kinetic energy :
KE = 1/2 I ω2 = 1/2 (1)(2)2 = 1/2 (1)(4) = 2 줄
2. 20kg 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?
알려진 바에 따르면:
질량 of cylinder pulley (m) = 20kg
The radius of cylinder (r) = 0.2 m
각속도 (ω) = 4 rad/s
구함: What is the rotational kinetic energy
해결책 ;
Formula of the moment inertia of cylinder :
I = 1/2 m r2
나는 = the moment of inertia (kg·m2), m = mass (kg), r = 반지름 (미터)
실린더 풀리의 관성 모멘트:
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 줄
3. A-10의 kg ball with radius of 0.1 m rotates at a constant of 10 rad/s. What is the kinetic energy of the ball.
알려진 바에 따르면:
질량 공의 (m) = 10 kg
Radius of ball (r) = 0.1 m
각속도 (ω) = 10 rad/s
구함: The rotational kinetic energy
솔루션 :
Formula of the moment of inertia :
I = (2/5) m r2
나는 = 관성 모멘트 (kg m2), m = mass (kg), r = 반지름 (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 줄
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 10의 cm.
알려진 바에 따르면:
질량 입자의 (m) = 0.5kg
The radius of ball (r) = 10 cm = 10/100 = 0.1 m
각속도 (ω) = 2 rad/s
구함: The rotational kinetic energy
솔루션 :
Moment of inertia for particle :
I = 씨2 = (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 줄
