sir Please Help me in 3 rd question them as rods.) 2. A grinding wheel is in the

Question

sir Please Help me in 3 rd question

them as rods.) 2. A grinding wheel is in the form of a uniform solid disk of radius 7 cm and mass 2 kg. It starts from rest and accelerates uniformly under the action of a constant 0.7 Nm torque that a motor supplies. a) How long does the wheel need to reach its operating speed of 1200 rev/min? b) Through how many revolutions does it turn while accelerating? 3. A thin, cylindrical rod I- 24 cm long with a mass of 1.2 kg has a ball of diameter d 8 cm and mass M 2 kg attached to one end. The arrangement is originally vertical and stationary, 2. with the ball on to as shown. The combination is free to pivot about the bottom end of the rodML0 2 after being given a slight nudge a) After the combination rotates through 90°, what is the rotational kinetic energy? b) What is the angular speed of the rod and ball? c) What is the linear speed of the center of mass of the ball? d) How does this compare to the speed had the ball fallen the same distance of 28 cm? 2 An electric motor turns a flywheel though a belt drive that joints a pulley on the motor and a pulley

Explanation / Answer

(a) PE is converted into KE. Measured relative to the pivot point, initial

PE = (1.20kg * 0.240m + 2.00kg * (0.0400 + 0.240)m) * 9.8m/s²

PE = 8.3104 J ? becomes the KE at 90º

(b) KE = 8.3104 J = ½Iw²

where

I = I_rod + I_sphere

I = mL²/3 + (2/5)MR² + M(R+L)² ? assuming the ball is solid

and invoking the parallel axis theorem

I = 1.20kg * (0.240m)² / 3 + (2/5) * 2.00kg * (0.0400m)² + 2.00kg * (0.28m)²

I = 0.18112 kg·m²

so

8.3104 J = ½ * 0.18112kg·m² * w²

w = 9.58 rad/s ? angular speed of rod and ball

(c) v = wr = 9.58rad/s * (0.240 + 0.0400)m = 2.68 m/s ?

(d) V = sqrt(2gh) = sqrt(2 * 9.8m/s² * 0.280m) = 2.34 m/s ?

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