(B) The acceleration of an object on the equator of a rotating star is the centripetal acceleration,given by $a = \omega^2 r$.Given frequency $n = 1 \

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(B) The acceleration of an object on the equator of a rotating star is the centripetal acceleration,given by $a = \omega^2 r$.Given frequency $n = 1 \, rev/sec$,so angular velocity $\omega = 2\pi n = 2\pi \, rad/sec$.The radius $r = 20 \, km = 20 \times 10^3 \, m$.Substituting these values into the formula:$a = (2\pi \times 1)^2 \times (20 \times 10^3)$$a = 4\pi^2 \times 20 \times 10^3$Using $\pi^2 \approx 10$:$a \approx 4 \times 10 \times 20 \times 10^3 = 800 \times 10^3 = 8 \times 10^5 \, m/sec^2$.

Class 11 Physics 2 Motion in a Plane Kinematics Circular Motion (Uniform Angular Accelaration)

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Certain neutron stars are believed to be rotating at about $1 \, rev/sec$. If such a star has a radius of $20 \, km$,the acceleration of an object on the equator of the star will be:

A
$20 \times 10^8 \, m/sec^2$
B
$8 \times 10^5 \, m/sec^2$
C
$120 \times 10^5 \, m/sec^2$
D
$4 \times 10^8 \, m/sec^2$

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2 Motion in a Plane

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Kinematics Circular Motion (Uniform Angular Accelaration)

The direction of angular acceleration of a body moving in a circle in the plane of the paper is

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If the position vector of a particle is $\vec{r} = (3\hat{i} + 4\hat{j}) \text{ m}$ and its angular velocity is $\vec{\omega} = (\hat{j} + 2\hat{k}) \text{ rad/s}$, then its linear velocity $\vec{v}$ is (in $\text{m/s}$):

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The angular acceleration of a wheel is $3 \ rad/s^2$. If its initial angular velocity is $2 \ rad/s$,what is the angular displacement (in $rad$) covered by it in $2 \ s$?

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In the $P^{\text{th}}$ second,a particle describes an angular displacement of $\beta \text{ rad}$. If it starts from rest,the angular acceleration is:

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$A$ wheel is subjected to uniform angular acceleration about its axis. Initially,its angular velocity is zero. In the first $2 \ s$,it rotates through an angle ${\theta _1}$. In the next $2 \ s$,it rotates through an additional angle ${\theta _2}$. The ratio of ${\theta _2}/{\theta _1}$ is:

MediumAIIMS 1985

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Certain neutron stars are believed to be rotating at about $1 \, rev/sec$. If such a star has a radius of $20 \, km$,the acceleration of an object on the equator of the star will be:

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