Question

A person travelling in a circular track of radius 100m,with tangential acceleration 2ms^-2. His angular acceleration is

Answer 1

Answer:

Given:

Radius of circular track = 100 m

Linear Acceleration ( tangential acceleration ) is 2 m/s².

To find:

Angular acceleration of the object

Concept:

Angular acceleration is an axial vector directed perpendicular to the plane in which object removes in circular trajectory.

It is the rotational analogue of tangential acceleration.

It is related to tangential acceleration just like angular Velocity is related to linear velocity.

Calculation:

$\huge{ \red{acc. = \alpha \times r}}$

$\huge{ \red{ = > \alpha = \frac{acc.}{r} }}$

$\huge{ \red{ = > \alpha = \frac{2}{100} }}$

$\huge{ \red{ = > \alpha = 0.02 \: rad {s}^{ - 2} }}$

Additional information :

• Tangential Acceleration is found by the vector product of angular acceleration and radius .
• So using thumb rule , the direction is obtained by moving the fore-fingers from direction of angular acceleration towards radius vector. The thumb denoted direction of Tangential Acceleration .

Answer 2

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$angular \: acceleration = \frac{ \alpha }{r} = \frac{2}{100} = 0.02 \: rad \: per \: sec$

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