A large number of adjectives end in -ic and -ical. In most cases, it is not easy to say which form is correct.

Here is a list of some adjectives ending in -ic.

academic
artistic
athletic
catholic
domestic
dramatic
emphatic
energetic
fantastic
linguistic
majestic
neurotic
pathetic
phonetic
public
tragic

Notes:
In older English, some of these words ended in -ical. Examples are: majestical, tragical and fantastical.

Adjectives ending in -ical

biological
chemical
critical
cynical
grammatical
logical
mathematical
mechanical
medical
musical
physical
radical
surgical
topical

Adjectives with both forms
Some adjectives can have both forms with no significant difference in meaning. Examples are:

arithmetic or arithmetical
egoistic or egoistical
fanatic or fanatical
geometric or geometrical
strategic or strategical

In some cases both forms exist, but there is usually a difference in meaning.

Classic and classical

Classic means ‘belonging to the highest class or degree’. Classical refers to the culture of ancient Greece or Rome. It may also refer to works of art of the so called ‘classical’ period in the 18th century.

I am studying classical languages.

Comic and comical

Comic refers to artistic comedy.
comic opera
Comical means ‘funny’.

She had a comical expression on her face.

Economic or economical

Economic refers to the science of economics.

Economic problems
Economic theory

Economical means ‘not wasting money’.

An economical little car

Politic and political

Politic means wise or prudent. Political means ‘connected with politics’.