Derive an expression for the moment of inertia of a thin uniform rod about an axis through its centre and perpendicular to
its length. Also determine the radius of gyration about the same axis.
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ꜰɪɢᴜʀᴇ 10.25 ᴄᴀʟᴄᴜʟᴀᴛɪᴏɴ ᴏꜰ ᴛʜᴇ ᴍᴏᴍᴇɴᴛ ᴏꜰ ɪɴᴇʀᴛɪᴀ ɪ ꜰᴏʀ ᴀ ᴜɴɪꜰᴏʀᴍ ᴛʜɪɴ ʀᴏᴅ ᴀʙᴏᴜᴛ ᴀɴ ᴀxɪꜱ ᴛʜʀᴏᴜɢʜ ᴛʜᴇ ᴄᴇɴᴛᴇʀ ᴏꜰ ᴛʜᴇ ʀᴏᴅ. λ=ᴍʟᴏʀᴍ=λʟ. λ = ᴍ ʟ ᴏʀ ᴍ = λ ʟ . ɪ=∫ʀ2ᴅᴍ=∫x2ᴅᴍ=∫x2λᴅx.
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Answer:
the moment of inertia is denoted by I
and I = mr²
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