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Chapter 1: Q12DQ (page 92)

In uniform circular motion, the acceleration is perpendicular to the velocity at every instant. Is this true when the motion is not uniformthat is, when the speed is not constant?

Short Answer

Expert verified

The statement is true that the acceleration is perpendicular to the velocity at every instant.

Step by step solution

01

Concept/Significance of acceleration of circular motion.

The amount of the centripetal force and the mass of a moving body in a circle define the acceleration.

02

Determination if the statement is true or not that the acceleration is perpendicular to the velocity at every instant.

Both of the acceleration and velocity at that moment should balance the force necessary to move the body in a circular direction.

Even though the speed is not constant in a non-uniform circular motion, the component of acceleration remains perpendicular to the initial velocity and pointed towards the circle's centre. Because the motion's speed isn't continuous, the centripetal acceleration isn't either. Wherever the speed is highest, the centripetal or radial acceleration is greatest. Another radial component of acceleration, a, which is parallel or tangential to the route and equal to the rate of change of its speed, exists.

Only when the particle acceleration vector is zero, which indicates the particle is moving in a straight path at constant speed, is the magnitude of vector acceleration zero.

Hence, the statement is true that the acceleration is perpendicular to the velocity at every instant.

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