Question

statement:when the particle moves with uniform speed in a circular path then its accelaration and velocity are constant
why this statement is wrong

Answer 1

Answer on Question #48568, Physics, Mechanics | Kinematics | Dynamics

Statement: when the particle moves with uniform speed in a circular path then its acceleration and velocity are constant.

Why this statement is wrong?

Solution:

A particle is in uniform circular motion if it travels in a circular path at a constant speed. Even though its speed remains constant, a particle in uniform circular motion is constantly accelerating. This can initially be a little counterintuitive, but it stems from the definition that acceleration is the rate of change of velocity which is a vector quantity, having both magnitude and direction. Since the direction of the speed continuously changes when a particle moves in a circular path, the velocity also continuously changes and hence there is a constant acceleration.

Figure: Velocity v and acceleration a in uniform circular motion at angular rate $\omega$ ; the speed is constant, but the velocity is always tangent to the orbit; the acceleration has constant magnitude, but always points toward the center of rotation.

Answer: Though the body's speed is constant, its velocity is not constant: velocity, a vector quantity, depends on both the body's speed and its direction of travel.

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