(3) The uniform thin disk of mass m-2kg and radius 2 m rotates about a fixed axi
ID: 1756694 • Letter: #
Question
(3) The uniform thin disk of mass m-2kg and radius 2 m rotates about a fixed axis through its mass center O. The disk is initially rotating at a counterclockwise angular velocity of 2 rad/s. Then a force of magnitude F-4 N is applied to the end of a rope tightly wrapped around the rim of the disk. The mass of the rope can be neglected. When the rope has been pulled down 8 m, the angular velocity of the disk is: (a) 2 rad/s (b) 4 rad/s 25 rads (d) 26 rad/s 0 4) The uniform thin disk of mass m-2kg and radiusr 2 m rotates about a fixed axis through its mass center O-The disk is initially rotating at a counterclockwise angular velocity of 2 rad/s. Then a force of magnitude F-4 N is applied to the end of a rope tightly wrapped around the rim of the disk. The mass of the rope can be neglected At the instant when the moment couple has been applied for 4 seconds, the angular velocity of the disk is: a) 4 rad/s clockwise b) 6 rad/s clockwise (c) 8 rad/s clockwise (d) 10 rad/s clockwiseExplanation / Answer
( 3 )
Given, that the force is applied of 4N for a distance of 8m.
Hence, work done by the force = Force * Displacement = 4 * 8 = 32 J
Work done = Change in Kinetic Energy of the disk = 0.5 * I * ( (w*w) - (2*2) )
Where, I is the Moment of Inertia = 0.5 * M * R * R = 0.5 * 2 * 2 * 2 = 4 kg sq.m
w is the final angular velocity and 2 is the initial radial velocity, considering counterclockwise direction to be positive.
So, 32 = 0.5 * 4 * ( (w*w) - 4 )
On solving, we get w = 4.47 rad/s, Hence, option (c) is correct
( 4 )
Given, that the force is applied of 4N for a duration of 4 seconds.
Impulse of the force = 4 * 4 = 16 Ns
Impulse = Change in angular momentum = I * ( w - 2 )
Where, I is the Moment of Inertia = 0.5 * M * R * R = 0.5 * 2 * 2 * 2 = 4 kg sq.m
w is the final angular velocity and 2 is the initial radial velocity, considering counterclockwise direction to be positive.
So, 16 = 4 * ( w - 2 )
On solving, we get, w = 6 rad/s, Hence, option (b) is correct.
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