A bicycle pump contains 200 cm3 of air and is connected to a bicycle tyre. The volume of the tyre is 800 cm3. The pressure of th
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The angular speed of the merry-go-round reduced more as the sandbag is
placed further from the axis than increasing the mass of the sandbag.
The rank from largest to smallest angular speed is presented as follows;
[m = 10 kg, r = 0.25·R]
⇩
[m = 20 kg, r = 0.25·R]
⇩
[m = 10 kg, r = 0.5·R]
⇩
[m = 10 kg, r = 0.5·R] = [m = 40 kg, r = 0.25·R]
⇩
[m = 10 kg, r = 1.0·R]
Reasons:
The given combination in the question as obtained from a similar question online are;
<em>1: m = 20 kg, r = 0.25·R</em>
<em>2: m = 10 kg, r = 1.0·R</em>
<em>3: m = 10 kg, r = 0.25·R</em>
<em>4: m = 15 kg, r = 0.75·R</em>
<em>5: m = 10 kg, r = 0.5·R</em>
<em>6: m = 40 kg, r = 0.25·R</em>
According to the principle of conservation of angular momentum, we have;
The moment of inertia of the merry-go-round, = 0.5·M·R²
Moment of inertia of the sandbag = m·r²
Therefore;
0.5·M·R²· = (0.5·M·R² + m·r²)·
Given that 0.5·M·R²· is constant, as the value of m·r² increases, the value of
decreases.
The values of m·r² for each combination are;
Combination 1: m = 20 kg, r = 0.25·R; m·r² = 1.25·R²
Combination 2: m = 10 kg, r = 1.0·R; m·r² = 10·R²
Combination 3: m = 10 kg, r = 0.25·R; m·r² = 0.625·R²
Combination 4: m = 15 kg, r = 0.75·R; m·r² = 8.4375·R²
Combination 5: m = 10 kg, r = 0.5·R; m·r² = 2.5·R²
Combination 6: m = 40 kg, r = 0.25·R; m·r² = 2.5·R²
Therefore, the rank from largest to smallest angular speed is as follows;
Combination 3 > Combination 1 > Combination 5 = Combination 6 >
Combination 2
Which gives;
[<u>m = 10 kg, r = 0.25·R</u>] > [<u>m = 20 kg, r = 0.25·R</u>] > [<u>m = 10 kg, r = 0.5·R</u>] > [<u>m = </u>
<u>10 kg, r = 0.5·R</u>] = [<u>m = 40 kg, r = 0.25·R</u>] > [<u>m = 10 kg, r = 1.0·R</u>].
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