| 1. |
What points do we conculdefrom dimensien at analysis?Explain the principal of homogeneity of dimensions. |
|
Answer» ᴘʀɪɴᴄɪᴘʟᴇ ᴏғ ʜᴏᴍᴏɢᴇɴᴇɪᴛʏ sᴛᴀᴛᴇs ᴛʜᴀᴛ ᴅɪᴍᴇɴsɪᴏɴs ᴏғ ᴇᴀᴄʜ ᴏғ ᴛʜᴇ ᴛᴇʀᴍs ᴏғ ᴀ ᴅɪᴍᴇɴsɪᴏɴᴀʟ ᴇϙᴜᴀᴛɪᴏɴ ᴏɴ ʙᴏᴛʜ sɪᴅᴇs sʜᴏᴜʟᴅ ʙᴇ ᴛʜᴇ sᴀᴍᴇ. ᴛʜɪs ᴘʀɪɴᴄɪᴘʟᴇ ɪs ʜᴇʟᴘғᴜʟ ʙᴇᴄᴀᴜsᴇ ɪᴛ ʜᴇʟᴘs ᴜs ᴄᴏɴᴠᴇʀᴛ ᴛʜᴇ ᴜɴɪᴛs ғʀᴏᴍ ᴏɴᴇ ғᴏʀᴍ ᴛᴏ ᴀɴᴏᴛʜᴇʀ ᴀᴘᴘʟɪᴄᴀᴛɪᴏɴs ᴏғ ᴅɪᴍᴇɴsɪᴏɴᴀʟ ᴀɴᴀʟʏsɪs ᴅɪᴍᴇɴsɪᴏɴᴀʟ ᴀɴᴀʟʏsɪs ɪs ᴀ ғᴜɴᴅᴀᴍᴇɴᴛᴀʟ ᴀsᴘᴇᴄᴛ ᴏғ ᴍᴇᴀsᴜʀᴇᴍᴇɴᴛ ᴀɴᴅ ɪs ᴀᴘᴘʟɪᴇᴅ ɪɴ ʀᴇᴀʟ-ʟɪғᴇ ᴘʜʏsɪᴄs. ᴡᴇ ᴍᴀᴋᴇ ᴜsᴇ ᴏғ ᴅɪᴍᴇɴsɪᴏɴᴀʟ ᴀɴᴀʟʏsɪs ғᴏʀ ᴛʜʀᴇᴇ ᴘʀᴏᴍɪɴᴇɴᴛ ʀᴇᴀsᴏɴs: ᴛᴏ ᴄʜᴇᴄᴋ ᴛʜᴇ ᴄᴏɴsɪsᴛᴇɴᴄʏ ᴏғ ᴀ ᴅɪᴍᴇɴsɪᴏɴᴀʟ ᴇϙᴜᴀᴛɪᴏɴ ᴛᴏ ᴅᴇʀɪᴠᴇ ᴛʜᴇ ʀᴇʟᴀᴛɪᴏɴ ʙᴇᴛᴡᴇᴇɴ ᴘʜʏsɪᴄᴀʟ ϙᴜᴀɴᴛɪᴛɪᴇs ɪɴ ᴘʜʏsɪᴄᴀʟ ᴘʜᴇɴᴏᴍᴇɴᴀ ᴛᴏ ᴄʜᴀɴɢᴇ ᴜɴɪᴛs ғʀᴏᴍ ᴏɴᴇ sʏsᴛᴇᴍ ᴛᴏ ᴀɴᴏᴛʜᴇʀ ʟɪᴍɪᴛᴀᴛɪᴏɴs ᴏғ ᴅɪᴍᴇɴsɪᴏɴᴀʟ ᴀɴᴀʟʏsɪs sᴏᴍᴇ ʟɪᴍɪᴛᴀᴛɪᴏɴs ᴏғ ᴅɪᴍᴇɴsɪᴏɴᴀʟ ᴀɴᴀʟʏsɪs ᴀʀᴇ: ɪᴛ ᴅᴏᴇsɴ’ᴛ ɢɪᴠᴇ ɪɴғᴏʀᴍᴀᴛɪᴏɴ ᴀʙᴏᴜᴛ ᴛʜᴇ ᴅɪᴍᴇɴsɪᴏɴᴀʟ ᴄᴏɴsᴛᴀɴᴛ. ᴛʜᴇ ғᴏʀᴍᴜʟᴀ ᴄᴏɴᴛᴀɪɴɪɴɢ ᴛʀɪɢᴏɴᴏᴍᴇᴛʀɪᴄ ғᴜɴᴄᴛɪᴏɴ, ᴇxᴘᴏɴᴇɴᴛɪᴀʟ ғᴜɴᴄᴛɪᴏɴs, ʟᴏɢᴀʀɪᴛʜᴍɪᴄ ғᴜɴᴄᴛɪᴏɴ, ᴇᴛᴄ. ᴄᴀɴɴᴏᴛ ʙᴇ ᴅᴇʀɪᴠᴇᴅ. ɪᴛ ɢɪᴠᴇs ɴᴏ ɪɴғᴏʀᴍᴀᴛɪᴏɴ ᴀʙᴏᴜᴛ ᴡʜᴇᴛʜᴇʀ ᴀ ᴘʜʏsɪᴄᴀʟ ϙᴜᴀɴᴛɪᴛʏ ɪs ᴀ sᴄᴀʟᴀʀ ᴏʀ ᴠᴇᴄᴛᴏʀ. |
|