A disc of mass M and radius R is free to rotate about its vertical axis as shown in the figure. A battery operated motor of negligible mass is fixed to this disc at a point on its circumference. Another disc of the same mass M and radius R 2 is fixed to

Question

A disc of mass M and radius R is free to rotate about its vertical axis as shown in the figure. A battery operated motor of negligible mass is fixed to this disc at a point on its circumference. Another disc of the same mass M and radius $\frac{R}{2}$ is fixed to the motor’s thin shaft. Initially, both the discs are at rest. The motor is switched on so that the smaller disc rotates at a uniform angular speed $ω$ . If the angular speed at which the large disc rotates is $\frac{ω}{n}$ , then the value of $n$ is ______. [2024]

Smart Achievers · Accepted Answer

(12)

Using conservation of angular momentum of the system (bigger + smaller disc) about the symmetric axis of large disc.

$\frac{1}{2} M {(\frac{R}{2})}^{2} ω - M (ω' R) . R - \frac{M R^{2}}{2} . ω' = 0$

$\Rightarrow \frac{ω}{8} = \frac{3 ω'}{2} \Rightarrow ω' = \frac{ω}{12}$

$Hence, the value of n = 12$

Solution

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Solution

Ans. (12) Using conservation of angular momentum of the system (bigger + smaller disc) about the symmetric axis of large disc. 12M(R2)2ω-M(ω'R).R-MR22.ω'=0 ⇒ω8=3ω'2⇒ω'=ω12 Hence, the value of n=12

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