1. An object has the د جورۍ شیبه of 1 kg m2 rotates at a constant angular speed of 2 rad/s. هغه څه چې د rotational kinetic energy of the object?
پیژندل شوی:
The moment of inertia (I) = 1 kg m2
د د زاویې سرعت (ω) = ۵۰ رادیو/ثانیې
SE busca: The rotational kinetic energy (KE)
حل:
The formula of the rotational kinetic energy :
KE = ۱/۴ زه ω2
KE = the rotational kinetic energy (kg m2/s2), I = the moment of inertia (kg m2), ω = the angular velocity (rad/s)
The rotational kinetic energy :
KE = 1/2 I ω2 = 1/2 (1)(2)2 = 1/2 (1)(4) = ۲،۳۷۶،۰۰۰ جول
2. A 20-kg 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?
پیژندل شوی:
ډله of cylinder pulley (m) = 20 kg
The radius of cylinder (r) = 0.2 m
The angular speed (ω) = 4 rad/s
غوښتل شوي: What is the rotational kinetic energy
Solution ;
Formula of the moment inertia of cylinder :
I = 1/2 m r2
زه = the moment of inertia (کیلو ګرامه متر2), m = mass (kg), r = ویډیو (meter)
The moment of inertia of cylinder pulley :
زه = ۱/۲ (۲)(۰.۱)2 = (10)(0.04) = 0.4 کیلو ګرامه متر2
The rotational kinetic energy of the pulley :
KE = 1/2 I ω2 = 1/2 (0.4)(4)2 = (۰.۴۴)(۵۰۰۰) = ۲،۳۷۶،۰۰۰ جول
3. A-10 کيلو ball with radius of 0.1 متر rotates at a constant of 10 rad/s. What is the kinetic energy of the ball.
پیژندل شوی:
ډله د توپ (m) = 10 kg
Radius of ball (r) = 0.1 m
زاویه سرعت (ω) = 10 rad/s
غوښتل شوي: The rotational kinetic energy
حل:
Formula of the moment of inertia :
I = (2/5) m r2
زه = د جورۍ شیبه (kg m2), m = mass (kg), r = ویډیو (m)
Moment of inertia of the ball :
زه = (۲/۵)(۲)(۰.۲)2 = (4)(0.01) = 0.04 کیلو ګرامه متر2
The rotational kinetic energy of the ball :
KE = 1/2 I ω2 = 1/2 (0.04)(10)2 = (۰.۴۴)(۵۰۰۰) = ۲،۳۷۶،۰۰۰ جول
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 cm.
پیژندل شوی:
ډله of particle (m) = 0.5 kg
The radius of ball (r) = 10 cm = 10/100 = 0.1 m
The angular speed (ω) = 2 rad/s
غوښتل شوي: The rotational kinetic energy
حل:
Moment of inertia for particle :
I = ښاغلی2 = (۰.۴۴)(۵۰۰۰)2 = (0.5)(0.01) = 0.005 کیلو ګرامه متر2
The rotational kinetic energy :
KE = 1/2 I ω2 = 1/2 (0.005)(2)2 = 1/2 (0.005)(4) = (۰.۴۴)(۵۰۰۰) = ۲،۳۷۶،۰۰۰ جول
