Calculate the dimension of Angular momentum

Physics

ScanSolve AI Answer

Answer

[M][L]2[T]−1[M][L]^2[T]^{-1}

Step-by-step solution

4 steps

To calculate the dimension of angular momentum, we can use its formula. One common formula for angular momentum (LL) is L=mvrL = mvr, where mm is mass, vv is velocity, and rr is the radius or distance.

  1. Identify the formula for angular momentum.

    We will use the formula: L=mvrL = mvr.

  2. Determine the dimensions of each variable.

    • Mass (mm) has dimensions of [M][M].
    • Velocity (vv) has dimensions of [L][T]−1[L][T]^{-1}.
    • Radius (rr) has dimensions of [L][L].

  3. Substitute the dimensions into the formula.

    [L]=[M]×[L][T]−1×[L][L] = [M] \times [L][T]^{-1} \times [L]

  4. Simplify the expression.

    [L]=[M][L]1+1[T]−1[L] = [M][L]^{1+1}[T]^{-1} [L]=[M][L]2[T]−1[L] = [M][L]^2[T]^{-1}

    The dimension of angular momentum is [M][L]2[T]−1[M][L]^2[T]^{-1}.

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