(B) The tangential acceleration $a_t$ is defined as the rate of change of the magnitude of velocity,given by $a_t = \frac{dv}{dt} = r \alpha$,where $r

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No,it is zero only when the angular speed is constant.

(B) The tangential acceleration $a_t$ is defined as the rate of change of the magnitude of velocity,given by $a_t = \frac{dv}{dt} = r \alpha$,where $r$ is the radius and $\alpha$ is the angular acceleration.If the angular speed $\omega$ is constant,then the angular acceleration $\alpha = \frac{d\omega}{dt} = 0$.Therefore,the tangential acceleration $a_t$ is zero only when the particle undergoes uniform circular motion,meaning the angular speed remains constant.

Class 11 Physics 3-2.Motion in Plane Kinematics Circular Motion (Uniform Angular Accelaration)

Medium

Is the tangential acceleration of a particle moving in a circular path always zero? Under what condition is it zero?

A
Yes,it is always zero.
B
No,it is zero only when the angular speed is constant.
C
No,it is zero only when the radius is constant.
D
No,it is zero only when the centripetal acceleration is zero.

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3-2.Motion in Plane

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Kinematics Circular Motion (Uniform Angular Accelaration)

$A$ wheel rotates with a uniform angular acceleration of $2.0 \ rad/s^2$. If the wheel starts from rest,the number of revolutions completed in the first $10 \ s$ will be approximately:

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$A$ particle of mass $m$ is moving in a circular path of constant radius $r$ such that its centripetal acceleration $a_c$ is varying with time $t$ as $a_c = k^2 r t^2$. The power delivered to the particle by the forces acting on it is:

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$A$ particle starts rotating from rest. Its angular displacement is expressed by the following equation $\theta = 0.025t^2 - 0.1t$,where $\theta$ is in radians and $t$ is in seconds. The angular acceleration of the particle is:

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When a ceiling fan is switched on,it makes $10$ rotations in the first $3\,s$. How many rotations will it make in the next $3\,s$? (Assume uniform angular acceleration)

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The angular speed of a motor wheel is increased from $1200 \; rpm$ to $3120 \; rpm$ in $16 \; s$.
$(i)$ What is its angular acceleration,assuming the acceleration to be uniform?
$(ii)$ How many revolutions does the engine make during this time?

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Is the tangential acceleration of a particle moving in a circular path always zero? Under what condition is it zero?

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$A$ wheel rotates with a uniform angular acceleration of $2.0 \ rad/s^2$. If the wheel starts from rest,the number of revolutions completed in the first $10 \ s$ will be approximately:

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The angular speed of a motor wheel is increased from $1200 \; rpm$ to $3120 \; rpm$ in $16 \; s$.
$(i)$ What is its angular acceleration,assuming the acceleration to be uniform?
$(ii)$ How many revolutions does the engine make during this time?