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Intro to Torque

A thin unifor...

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A thin uniform rod of length 1m and mass 500 g is attached to a uniform disc of diameter 20 cm and mass 100 g at one end as shown in the figure. The dis†an ce of center of mass from the free end of the rod is

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As shown below, a uniform disc is mounted to a fixed axle and is free to rotate without friction. A thin uniform rod is rigidly attached to the disc so that it will rotate with the disc. A block is attached to the rod.

Disc : mass = 3m, radius = R, moment of inertia about center $I_{D} = \frac{3}{2} m R^{2}$

Rod : mass = m, length = 2R, moment of inertia about one end $I_{R} = \frac{4}{3} m R^{2}$

Block : mass 2m

The system is held in equilibrium with the rod at an angle $θ_{0}$ to the vertical, as shown above, by a horizontal string of negligible mass one end attached to the disc and the other to a wall.

The tension in the string is

Q. A metaI rod of length '

L

m

' is pivoted at one end. A thin disk of mass '

M

^{'} R^{'} (< L)

is attached at its center to the free end of the rod. Consider two ways the disc is attached: (case A) The disc is not free to rotate about its center and (case B) the disc is free to rotate about its center. The rod-disc system performs SHM in vertical plane after being released from the same displaced position. Which of the following statement(s) is (are) true?

Q. A metal rod of length 'L' and mass "

m

is pivoted at one end. A thin disk of mass '

M

R^{'} (< L)

is attached at its center to the free end of the rod. Consider two ways the disc is attached: (case A) The disc is not free to rotate about its center and (case

B)

the disc is free to rotate about its center. The rod-disc system performs SHM in vertical plane after being released from the same displaced position. Which of the following statement(s) is (are) true?

Q. A rod of length of 1 m is attached to the string at its mid point. A 6 kg mass is attached to end of the rod and another mass M is hung at a distance of 30 cm from the center of the rod as shown in the figure. Assume mass of rod is negligible. Find out the value of M.

Q. A uniform rod is hinged at one end to a wall and hangs through a rope attached to the other end as shown in the figure. Mass of rod is 80 kg and a carpenter of mass 60 kg is sitting at

\frac{3 l}{4}

from the hinged end. Tension in supporting rope is

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