Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
Find the dimensions of (a) density, (b) impulse (force times time), (c) surface tension (force per length), (d) angular velocity. Give the power of in each.
The dimensions of a quantity are the powers of , and in it, found from any formula for it: multiplying adds the powers, dividing subtracts them, and pure numbers have none.
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. (a) Density : .
Step 2. (b) Impulse : , like momentum.
Step 3. (c) Surface tension : , no length left.
Step 4. (d) Angular velocity , and an angle is a pure number: .
Answer: (a) . (b) . (c) . (d) . The powers of L are , , and .
Watch out. Angular velocity is measured in rad/s, but the radian is not a dimension.
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