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[Maximum number: 4]

A student models a rotating dancer using a system that consists of a vertical cylinder, a horizontal rod and two spheres.

The cylinder rotates from rest about the central vertical axis. A rod passes through the cylinder with a sphere on each side of the cylinder. Each sphere can move along the rod. Initially the spheres are close to the cylinder.

A horizontal force of 50 N is applied perpendicular to the rod at a distance of 0.50 m from the central axis. Another horizontal force of 40 N is applied in the opposite direction at a distance of 0.20 m from the central axis. Air resistance is negligible.

(a)

When the system has reached its maximum angular speed, the two forces are removed. The spheres now move outward, away from the central axis.

[ 4 ]

(i)

Outline why the angular speed $\omega$ decreases when the spheres move outward.

[ 2 ]

moment of inertia increases

Angular momentum is conserved

Marking guidance:

Allow algebraic expressions e.g. $\omega=\frac{L}{I}$ so $\omega$ decreases for MP2

(ii)

When the spheres move outward, the angular speed decreases from $20 \mathrm{rad} \mathrm{s}^{-1}$ to $12 \mathrm{rads}^{-1}$ . Calculate the percentage change in rotational kinetic energy that occurs when the spheres move outward.

[ 2 ]

$\begin{aligned} & \boldsymbol{«} \mathrm{E}_{\mathrm{k}}=» \frac{1}{2} L \omega_{1}=1 / 2 L \omega_{2} & \boldsymbol{O} \boldsymbol{R} & \frac{E_{k 1}}{E_{k 2}}=\frac{\omega_{1}}{\omega_{2}} \end{aligned}$

OR

« L is constant so» $E_{\mathrm{k}}$ is proportional to $\omega$

40 \% «energy loss»

MP1 is for understanding that angular momentum is constant so change in rotational kinetic energy is proportional to change in angular velocity

Award [0] if $E=0.5 \mathrm{I} \omega^{2}$ is used with the same I value for both values of E

Award [2] for BCA

IB Physics HL A 4 10 Hl Angular Momentum Conservation Topic Practice

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IB Physics HL A 4 10 Hl Angular Momentum Conservation Topic Practice

Learn this topic

Question 1

Question (a)

Question (i)

Question (ii)