Question

Derive the expression for the acceleration of a particul performing uniform circular motion​

Answer 1

ᕙ(⇀‸↼‶)ᕗ

• ᴄʜᴏᴛᴇ ᴍᴀʀᴇ ᴛᴏ ʙʜᴀᴅᴇ ʙʜᴀɪ ᴛʜᴇ ᴊɪɴᴋɪ ᴅᴇᴀᴛʜ ʜᴏ ɢʏɪ

• ᴏʀʀ ᴀʙ ɴᴀ ʙᴀᴅᴀ ʙʜᴀɪ ʜᴇ ᴏʀʀ ɴᴀ ᴄʜᴏᴛᴀ ᴛᴏ ғᴜʀ ᴍᴜᴊʜᴇ ᴋʏᴀ ᴋᴀʟɴᴀ ᴄʜᴀɪʏᴇ ʙᴏʟ

• ɪsʟɪʏᴇ sᴀᴅ ᴍᴀᴛ ʜᴏ ᴄʜᴏᴛᴇ

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ᴇxᴘʀᴇssɪᴏɴ ғᴏʀ ᴄᴇɴᴛʀɪᴘᴇᴛᴀʟ ᴀᴄᴄᴇʟᴇʀᴀᴛɪᴏɴ ʙʏ ᴄᴀʟᴄᴜʟᴜs ᴍᴇᴛʜᴏᴅ: ɪ. sᴜᴘᴘᴏsᴇ ᴀ ᴘᴀʀᴛɪᴄʟᴇ ɪs ᴘᴇʀғᴏʀᴍɪɴɢ ᴜ.ᴄ.ᴍ ɪɴ ᴀɴᴛɪᴄʟᴏᴄᴋᴡɪsᴇ ᴅɪʀᴇᴄᴛɪᴏɴ. ᴛʜᴇ ᴄᴏ-ᴏʀᴅɪɴᴀᴛᴇ ᴀxᴇs ᴀʀᴇ ᴄʜᴏsᴇɴ ᴀs sʜᴏᴡɴ ɪɴ ᴛʜᴇ ғɪɢᴜʀᴇ. ʟᴇᴛ, ᴀ = ɪɴɪᴛɪᴀʟ ᴘᴏsɪᴛɪᴏɴ ᴏғ ᴛʜᴇ ᴘᴀʀᴛɪᴄʟᴇ ᴡʜɪᴄʜ ʟɪᴇs ᴏɴ ᴘᴏsɪᴛɪᴠᴇ x-ᴀxɪs ᴘ = ɪɴsᴛᴀɴᴛᴀɴᴇᴏᴜs ᴘᴏsɪᴛɪᴏɴ ᴀғᴛᴇʀ ᴛɪᴍᴇ ᴛ θ = ᴄᴏʀʀᴇsᴘᴏɴᴅɪɴɢ ᴀɴɢᴜʟᴀʀ ᴅɪsᴘʟᴀᴄᴇᴍᴇɴᴛ ω = ᴄᴏɴsᴛᴀɴᴛ ᴀɴɢᴜʟᴀʀ ᴠᴇʟᴏᴄɪᴛʏ → ʀ ʀ→ = ɪɴsᴛᴀɴᴛᴀɴᴇᴏᴜs ᴘᴏsɪᴛɪᴏɴ ᴠᴇᴄᴛᴏʀ ᴀᴛ ᴛɪᴍᴇ ᴛ ɪɪ. ғʀᴏᴍ ᴛʜᴇ ғɪɢᴜʀᴇ, → ʀ = ^ ɪ x + ^ ᴊ ʏ ʀ→=ɪ^x+ᴊ^ʏ ᴡʜᴇʀᴇ, ^ ɪ ɪ^ ᴀɴᴅ ^ ᴊ ᴊ^ ᴀʀᴇ ᴜɴɪᴛ ᴠᴇᴄᴛᴏʀs ᴀʟᴏɴɢ x-ᴀxɪs ᴀɴᴅ ʏ-ᴀxɪs ʀᴇsᴘᴇᴄᴛɪᴠᴇʟʏ. ɪɪɪ. ᴀʟsᴏ, x = ʀ ᴄᴏs θ ᴀɴᴅ ʏ = ʀ sɪɴ θ ɪᴠ. ᴠᴇʟᴏᴄɪᴛʏ ᴏғ ᴛʜᴇ ᴘᴀʀᴛɪᴄʟᴇ ɪs ɢɪᴠᴇɴ ᴀs ʀᴀᴛᴇ ᴏғ ᴄʜᴀɴɢᴇ ᴏғ ᴘᴏsɪᴛɪᴏɴ ᴠᴇᴄᴛᴏʀ. ᴠ. ғᴜʀᴛʜᴇʀ, ɪɴsᴛᴀɴᴛᴀɴᴇᴏᴜs ʟɪɴᴇᴀʀ ᴀᴄᴄᴇʟᴇʀᴀᴛɪᴏɴ ᴏғ ᴛʜᴇ ᴘᴀʀᴛɪᴄʟᴇ ᴀᴛ ɪɴsᴛᴀɴᴛ ᴛ ɪs ɢɪᴠᴇɴ ʙʏ, ᴠɪ. ғʀᴏᴍ ᴇǫᴜᴀᴛɪᴏɴ () ᴀɴᴅ (), → ᴀ ᴀ→ = − ω → ʀ −ωʀ→ ɴᴇɢᴀᴛɪᴠᴇ sɪɢɴ sʜᴏᴡs ᴛʜᴀᴛ ᴅɪʀᴇᴄᴛɪᴏɴ ᴏғ ᴀᴄᴄᴇʟᴇʀᴀᴛɪᴏɴ ɪs ᴏᴘᴘᴏsɪᴛᴇ ᴛᴏ ᴛʜᴇ ᴅɪʀᴇᴄᴛɪᴏɴ ᴏғ ᴘᴏsɪᴛɪᴏɴ ᴠᴇᴄᴛᴏʀ. ᴠɪɪ. ᴍᴀɢɴɪᴛᴜᴅᴇ ᴏғ ᴄᴇɴᴛʀɪᴘᴇᴛᴀʟ ᴀᴄᴄᴇʟᴇʀᴀᴛɪᴏɴ ɪs ɢɪᴠᴇɴ ʙʏ, ᴀ = ωʀ ᴀs ω = ᴠ ʀ ᴠʀ ∴ ᴀ = ᴠ ʀ ∴ᴀ=ᴠʀ ɴᴏᴛᴇ: ʀᴇᴀᴅ ᴍᴏʀᴇ ᴏɴ sᴀʀᴛʜᴀᴋs.ᴄᴏᴍ - ʜᴛᴛᴘs://ᴡᴡᴡ.sᴀʀᴛʜᴀᴋs.ᴄᴏᴍ//ᴇxᴘʀᴇssɪᴏɴ-ᴄᴇɴᴛʀɪᴘᴇᴛᴀʟ-ᴀᴄᴄᴇʟᴇʀᴀᴛɪᴏɴ-ᴘᴀʀᴛɪᴄʟᴇ-ᴘᴇʀғᴏʀᴍɪɴɢ-ᴜɴɪғᴏʀᴍ-ᴄɪʀᴄᴜʟᴀʀ-ᴍᴏᴛɪᴏɴ-ᴄᴀʟᴄᴜʟᴜs

Answer 2

particul performing uniform circular motion