Download App

Rotational Dynamics — Physics STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 SciencePhysicsRotational Dynamics3 Marks
Question
A ballet dancer spins about a vertical axis at $2.5 \pi \mathrm{rad} / \mathrm{s}$ with his arms outstretched. With the arms folded, the MI about the same axis of rotation changes by $25 \%$. Calculate the new speed of rotation in rpm.
✓

Answer

Let $I_1, w_1$, and $f_1$, be the moment of inertia, angular velocity and frequency of rotation of the ballet dancer with arms outstretched, and $\mathrm{I}_2, \mathrm{w}_2$ and $\mathrm{f}_2$ be the corresponding quantities with arms folded.
Data : $\omega_1=2.5 \pi \mathrm{rad} / \mathrm{s}$
Since moment of inertia with arms folded is less than that with arms outstretched,
$
\begin{aligned}
I_2 & <I_1 \\
\therefore I_2 & =I_1-0.25 I_1=0.75 I_1=\frac{3}{4} I_1 \\
\omega_1 & =2 \pi f_1=2.5 \pi \\
\therefore f_1 & =\frac{2.5 \pi}{2 \pi}=\frac{5}{4} \mathrm{~Hz}
\end{aligned}
$
According to the principle of conservation of angular momentum, $I_1 \omega_1=I_2 \omega_2$
$
\therefore I_1\left(2 \pi f_1\right)=I_2\left(2 \pi f_2\right)
$
The new frequency of rotation is
$
\begin{aligned}
f_2=\frac{I_1 f_1}{I_2}=\frac{4}{3} \times \frac{5}{4}=\frac{5}{3} \mathrm{~Hz} & =\frac{5}{3} \times 60 \mathrm{rpm} \\
& =100 \mathrm{rpm}
\end{aligned}
$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "Answer the following in Brief" from Rotational Dynamics→Rotational Dynamics — all question types→Physics STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

On what factors does the frequency of a conical pendulum depend? Is it independent of some factors?
→
A moving coil galvanometer has been fitted with a rectangular coil having $50$ turns and dimensions $5\ cm \times 3\ cm$. The radial magnetic field in which the coil is suspended is of $0.05 Wb / m ^2$. The torsional constant of the spring is $1.5$ $\times 10^{-9} Nm /$ degree. Obtain the current required to be passed through the galvanometer so as to produce a deflection of $30^{\circ}$.
→
The equation of motion of a particle executing SHM is $x = a \sin \left(\frac{\pi}{6} t\right)+ b \cos \left(\frac{\pi}{6} t\right)$, where a $=3 cm$ and $b =4 cm$. Express this equation in the form $x = A \sin \left(\frac{\pi}{6} t+\phi\right)$. Hence, find $A$ and $\varphi$.
→
A current-carrying coil with magnetic moment $\vec{M}\left( M =5 A \cdot m ^2\right)$ is placed in a uniform magnetic field of induction $\vec{B}\left( B =0.2 Wb / m ^2\right)$ such that the angle between $\vec{M}$ and $\vec{B}$ is $30^{\circ}$. What is the torque acting on the coil?
→
A metal cube of side $2 \mathrm{~cm}$ emits $672 \mathrm{~J}$ of heat in $100 \mathrm{~s}$ at a certain temperature. Calculate its emissive power (radiant power) at that temperature.
→
Define: (a) Inductive reactance (b) Capacitive reactance (c) Impedance.
→
A cube of marble having each side $1$ cm is kept in an electric field of intensity $300 V / m$. Determine the energy contained in the cube of dielectric constant $8$ . (Given: $\varepsilon_o=8.85 \times 10^{-12} C ^2 / Nm ^2$ )
→
A metal plate of length $10 \mathrm{~cm}$ and breadth $5 \mathrm{~cm}$ is in contact with a layer of oil $1 \mathrm{~mm}$ thick. The horizontal force required to move it with a velocity of $4 \mathrm{~cm} / \mathrm{s}$ along the surface of the oil is $0.32 \mathrm{~N}$. Find the coefficient of viscosity of the oil. Also express it in poise.
→
A long solenoid of length l, cross-sectional area A and having N1 turns (primary coil) has a small coil of N2 turns (secondary coil) wound about its centre. Determine the Mutual inductance (M) of the two coils.
→
Two moles of a gas expand isothermally at $300 K$. If the initial volume of the gas is $23 L$ and the final volume is $46 L$, find the work done by the gas on its surroundings. ( $R=8.314$ $J / mol . K )$
→