Rotational Mechanics Question

Q. A uniform metre stick of mass M is hinged at one end and supported in the horizontal direction by a string attached to the other end. What should be the initial angular acceleration of the stick if the string is cut?

a. $\frac{3}{2}g\hspace{2 mm}rad\hspace{1 mm}s^{-2}$

b. $g\hspace{2 mm}rad\hspace{1 mm}s^{-2}$

c. $3g\hspace{2 mm}rad\hspace{1 mm}s^{-2}$

d. $4g\hspace{2 mm}rad\hspace{1 mm}s^{-2}$

The answer given was a... But i think it should be c. Pls solve this..

Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

Markdown	Appears as
`italics` or `_italics_`	italics
`bold` or `__bold__`	bold
- bulleted - list	bulleted list
1. numbered 2. list	numbered list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1 paragraph 2	paragraph 1 paragraph 2
`[example link](https://brilliant.org)`	example link
`> This is a quote`	This is a quote
# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"	# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"

Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

The stick has moment of inertia $I = \tfrac{1}{3}ML^2$ about the hinge. The weight of the stick is $W = Mg$ and it acts at the center of mass which is $d = \tfrac{1}{2}L$ from the hinge. Initially, the weight is perpendicular to the stick. So, the total torque initially is $\tau = Wd = \tfrac{1}{2}MgL$ . Since $\tau = I\alpha$ , the initial angular acceleration is $\alpha = \dfrac{\tau}{I} = \dfrac{\tfrac{1}{2}MgL}{\tfrac{1}{3}ML^2} = \dfrac{3g}{2L}$ . Plug in $L = 1m$ to get the answer.

Jimmy Kariznov - 7 years, 10 months ago

Thanks...

Krishna Jha - 7 years, 10 months ago

nice......just mingle around the formulas...as simple as that.

Max B - 7 years, 1 month ago

But L=1m is not given right??

Joe Bobby - 5 years, 8 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$