Question

(Figure 1) shows a 100 g puck revolving at 190 rpm on a 20-cm-radius circle on a frictionless table. A string attached to the puck passes through a hole in the middle of the table. The end of the string below the table is then slowly pulled down until the puck is revolving in a 15-cm-radius circle.
How many revolutions per minute does the puck make at this new radius?​

Answer 1

The puck made 338 revolutions per minute at this new radius.

The law of conservation of angular momentum posits that if there is no external torque acting on material or an object in space, then no difference will occur in the angular momentum.

Since there is no external torque in the direction of the motion from the given information;

∴

By applying the conservation of angular momentum:

Initial angular momentum = Final angular momentum

$\mathbf{I_1\omega_1 = I_2\omega_2}$

$\mathbf{mr_1^2 \omega_1 = mr_2^2\omega_2}$

$\mathbf{\omega_2 = (\dfrac{r_1}{r_2} )^2 \omega_1}$

where;

• r₁ = 20 cm = 0.20 m
• r₂ = 15 cm = 0.15 cm
• ω₁ = 190 rpm

$\mathbf{\omega_2 = (\dfrac{0.2}{0.15} )^2 \times 190 \ rpm}$

$\mathbf{\omega_2 = 1.778 \times 190}$

$\mathbf{\omega_2 =337.82 \ rpm}$

$\mathbf{\omega_2 \simeq 338 \ rpm}$

Therefore, we can conclude that the puck made 338 revolutions per minute at this new radius.

Learn more about the conservation of angular momentum here:

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