sliding window partitioning on date field
Starting from the fact that I wouldn't partition on a column which is not used in a where clause, yes, your clustered index will have to change to include the log_date into its key columns, and yes, you can still query it filtering on ID only. I'd still suggest to include the partitioning column into your where clause to leverage partition elimination.

It's explained to much detail here: https://docs.microsoft.com/en-us/sql/relational-databases/partitions/partitioned-tables-and-indexes?view=sql-server-2017