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Concepts Of Physics MCQ Edition [Volume 1]

Exam: Concepts Of Physics MCQ Edition [Volume 1]
Subject: Physics
Chapter: Rotational Mechanics

Concepts Of Physics MCQ Edition [Volume 1] · Physics · Rotational Mechanics

A disc rotates about its axis with a uniform angular acceleration...

A disc rotates about its axis with a uniform angular acceleration of

4 \text{ rad/s}^2

. Determine the radial and tangential accelerations of a particle located

1 \text{ cm}

from the axis at the end of the first second after the disc begins rotating.

Options

A $16 \text{ cm/s}^2$ , $4 \text{ cm/s}^2$
B $4 \text{ cm/s}^2$ , $16 \text{ cm/s}^2$
C $4 \text{ cm/s}^2$ , $4 \text{ cm/s}^2$
D $8 \text{ cm/s}^2$ , $4 \text{ cm/s}^2$

Correct answer

A. $16 \text{ cm/s}^2$ , $4 \text{ cm/s}^2$

Step-by-step solution

Given initial angular velocity

\omega_0 = 0

and angular acceleration

\alpha = 4 \text{ rad/s}^2

.

The angular velocity at time

t = 1 \text{ s}

is given by:

\omega = \omega_0 + \alpha t = 0 + 4 \times 1 = 4 \text{ rad/s}

The radial acceleration

a_r

of a particle at a distance

r = 1 \text{ cm}

from the axis is:

a_r = \omega^2 r = (4)^2 \times 1 = 16 \text{ cm/s}^2

The tangential acceleration

a_t

of the particle is:

a_t = \alpha r = 4 \times 1 = 4 \text{ cm/s}^2

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