Dimensional Analysis

Question 1

What are the dimensions of velocity and acceleration?

Answer 1

[Velocity] = LT^-1

[Acceleration] = LT^-2

Question 2

What is the equation of density?

Answer 2

Density (p) = mass / volume

Question 3

What is the dimension of density?

Answer 3

[p] = [mass] / [volume]
= M/L^3
= ML^-3

Question 4

What is the dimension for force?

Answer 4

[F] = [m][a] = MLT^-2

Question 5

What is the equation of pressure?

Answer 5

Pressure = force / area

Question 6

What is the dimension for pressure

Answer 6

[p] = [F] / [A]
= MLT^-2 / L^2
= ML^-1T^-2

Question 7

What is the dimension of Energy?

Answer 7

[energy] = [m][v^2]
= m (LT^-1)^2
= mL^2T^-2

Question 8

What is the equation for energy?

Answer 8

KE = 0.5mv^2

Question 9

What are the dimension of an angle, theta?

Answer 9

[theta] = [s] / [r]

Therefore, theta is dimensionless

Question 10

What is the dimension of frequency?

Answer 10

[F] = 1/ [s]

= T^-1

Question 11

What is the dimension for Angular speed?

Answer 11

[Angular speed] = T^-1

Question 12

What are the general steps for using dimensional analysis in modelling?

Answer 12

1. suggest a formula based on a product of (unknown) powers of quantities
2. Call these unknown alpha, beta and gamma
3. Include a dimensionless constant
4. Use indices to compare powers of M, L & T in the formula
5. Deduce alpha, beta and gamma

Question 13

What is the equation of power?

Answer 13

Power = work done / time taken

P = E / T
= mc^2 / t

Question 14

What is the dimensional equation of power?

Answer 14

P = E / T
= ML^2T^-2 / T
= ML^2T^-3

Question 15

What is the dimensional equation of weight?

Answer 15

Weight = mass * acceleration
= [mass] * [acceleration]
= M* LT^-2
= MLT^-2