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problems with solutions

Topic:Rotational Mechanics

I.D Level Problem Problem Topic
43 High school Consider a too-small space habitat that consists of a rotating cylinder of radius of 4m. If a man standing inside is 2m tall and his feet are at 1g, what is the g force at the elevation of his head? . . . continues
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Rotational Mechanics
278 High school A 3.0 kg mass is positioned at (0,0.8) , and a 1.0 kg is positioned at (12,0). What are the coordinates of a 4.0 kg mass which will result in the centre of mass of the system of three masses being located at the origin , (0,0) ?

a) (-3.0,-6.0)

b) (-12,-8.0)

c) (3.0,6.0)

d) (-6, -3)

. . . continues
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Rotational Mechanics
556 High school A bicycle has wheel of radius 0.28 m . Each wheel has a rotational inertia of 0.094 kg.m^2 about its axle . The total mass of the bicycle including the wheels and the rider is 79 kg . When coasting at constant speed , What fraction of the total kinetic energy of the bicycle (including rider) is the rotational kinetic energy of the wheels ? . . . continues
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Rotational Mechanics
557 High school A flywheel of mass 185 kg has an effective radius of 0.62 m (assume the mass is concentrated along a circumference located at the effective radius of the flywheel )

(a) What torque is required to bring this wheel from rest to a speed of 122 rpm in a time interval of 28.2 s ?

(b) How much work is done during the 28.2 s ?

. . . continues
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Rotational Mechanics
558 High school A grinding wheel , with a mass of 21.5 kg and a radius of 23.2 cm, is a uniform cylindrical disk .

(a) Find the rotational inertia of the wheel about its central axis .

(b) When the grinding wheel’s motor is turned off , friction causes the wheel to slow from 1200 rpm to rest in 59.7 S . What torque must the motor provide to acceler . . . continues
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Rotational Mechanics
559 High school A playground merry-go-ground , made in the shape of a solid disk , has a diameter of 2.54 m and a mass of 352.5 kg . Two children , each of mass 30.1 kg , sit on opposite sides at the edge of the platform . Approximately the children as point masses .

(a) What torque is required to bring the merry-go-round from rest to 29 rpm in 19.9 S ?

. . . continues
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Rotational Mechanics
560 High school A solid sphere of mass 0.603 kg rolls without slipping along a horizontal surface with a translation speed of 5.31 m/s . It comes to an incline that makes an angle of 35 degree with the horizontal surface .

(a) What is the total energy of the rolling sphere ? Neglect energy losses due to friction .

(b) To what vertical height above . . . continues
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Rotational Mechanics
561 High school The string in a yo-yo is wound around an axle of radius 0.533 cm . The yo-yo has both rotational and translational motion , like a rolling object , and has mass 0.225 kg and outer radius 1.96 cm . Starting from rest , it rotates and falls a distance of 1.42 m ( the length of the string ). Assume for simplicity that the yo-yo is a uniform circular d . . . continues
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Rotational Mechanics
562 High school A figure skater is spinning at a rate of 1.0 rev/s with her arms outstretche . She then draws her arms in to her chest , reducing her rotational inertia to 68% of its original value . What is her new rate of rotation ? . . . continues
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Rotational Mechanics
563 High school A solid cylindrical disk is to be used as a stabilizer in a ship . By using a massive disk rotating in the hold of the ship , the captain knows that a large torque is required to tilt its angular momentum vector . The mass of the disk to be used is 1.62 x 10^5 kg and it has a radius of 2.05m . If the cylinder rotates at 300.0 rpm , what is the magn . . . continues
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Rotational Mechanics
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