(A) Length of the string,$r = 80\; cm = 0.8\; m$.Number of revolutions $= 14$,Time taken $= 25\; s$.Frequency,$\nu = \frac{\text{Number of revolutions

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$9.91\; m/s^2$ directed towards the center

(A) Length of the string,$r = 80\; cm = 0.8\; m$.Number of revolutions $= 14$,Time taken $= 25\; s$.Frequency,$\nu = \frac{\text{Number of revolutions}}{\text{Time taken}} = \frac{14}{25}\; Hz$.Angular frequency,$\omega = 2\pi\nu = 2 \times \frac{22}{7} \times \frac{14}{25} = \frac{88}{25}\; rad/s = 3.52\; rad/s$.Centripetal acceleration,$a_c = \omega^2 r = (3.52)^2 \times 0.8$.$a_c = 12.3904 \times 0.8 = 9.91232\; m/s^2 \approx 9.91\; m/s^2$.The direction of centripetal acceleration is always directed along the radius towards the center of the circular path.

Class 11 Physics 3-2.Motion in Plane Non-uniform Circular Motion (Centrifugal/Centripetal and tangential Accelaration)

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$A$ stone tied to the end of a string $80\; cm$ long is whirled in a horizontal circle with a constant speed. If the stone makes $14$ revolutions in $25\; s$,what is the magnitude and direction of acceleration of the stone?

A
$9.91\; m/s^2$ directed towards the center
B
$8.91\; m/s^2$ directed towards the center
C
$7.91\; m/s^2$ directed towards the center
D
$6.91\; m/s^2$ directed towards the center

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3-2.Motion in Plane

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Non-uniform Circular Motion (Centrifugal/Centripetal and tangential Accelaration)

The velocity and acceleration vectors of a particle undergoing circular motion are $\overrightarrow{v} = 2 \hat{i} \text{ m/s}$ and $\overrightarrow{a} = 2 \hat{i} + 4 \hat{j} \text{ m/s}^2$ respectively at an instant of time. The radius of the circle is $........ \text{ m}$.

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$A$ car is moving at a speed of $40\,m/s$ on a circular track of radius $400\,m.$ This speed is increasing at the rate of $3\,m/s^2.$ The acceleration of the car is ........ $m/s^2$.

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$A$ car is moving on a circular path of radius $500 \ m$ with a speed of $30 \ m/s$. If the speed is increasing at a rate of $2 \ m/s^2$,the net acceleration will be ......... $m/s^2$.

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$A$ particle moves in the $xy$-plane with velocity $\vec{v} = x \hat{i} + yt \hat{j}$. At $t = \frac{x \sqrt{3}}{y}$,the tangential and normal accelerations are:

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In non-uniform circular motion, the ratio of radial acceleration to tangential acceleration is (where $V$ is the velocity, $r$ is the radius, and $\alpha$ is the angular acceleration).

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$A$ stone tied to the end of a string $80\; cm$ long is whirled in a horizontal circle with a constant speed. If the stone makes $14$ revolutions in $25\; s$,what is the magnitude and direction of acceleration of the stone?

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The velocity and acceleration vectors of a particle undergoing circular motion are $\overrightarrow{v} = 2 \hat{i} \text{ m/s}$ and $\overrightarrow{a} = 2 \hat{i} + 4 \hat{j} \text{ m/s}^2$ respectively at an instant of time. The radius of the circle is $........ \text{ m}$.

$A$ car is moving at a speed of $40\,m/s$ on a circular track of radius $400\,m.$ This speed is increasing at the rate of $3\,m/s^2.$ The acceleration of the car is ........ $m/s^2$.

$A$ car is moving on a circular path of radius $500 \ m$ with a speed of $30 \ m/s$. If the speed is increasing at a rate of $2 \ m/s^2$,the net acceleration will be ......... $m/s^2$.

$A$ particle moves in the $xy$-plane with velocity $\vec{v} = x \hat{i} + yt \hat{j}$. At $t = \frac{x \sqrt{3}}{y}$,the tangential and normal accelerations are:

In non-uniform circular motion, the ratio of radial acceleration to tangential acceleration is (where $V$ is the velocity, $r$ is the radius, and $\alpha$ is the angular acceleration).

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