Question

Which of the following statements is false for a particle moving in a circle at a constant angular speed?
A. The acceleration vector is tangent to the circle
B. The acceleration vector is normal to the circle
C. The acceleration vector points to the center of the circle
D. The velocity and acceleration vectors are perpendicular to each other

Answer 1

Hint: Before we start addressing the problem, we need to know about the acceleration and velocity of a particle. Acceleration of a particle is defined as the rate of change of velocity with respect to time. Velocity usually refers to the displacement of the object per unit of time.

Complete step by step solution:
If we consider option A it says that the acceleration vector is tangent to the circle, but if a circle is moving in a circle acceleration vector is always towards the center, but not tangent to the circle. Therefore, option 1 is false.

For a 2d circular surface, the normal is nothing but a line perpendicular to the tangent at a point that is nothing but radial to the circle. So, option B is also correct. When a particle is moving in a circle then the acceleration of the particle is always towards the center and the velocity will always be tangential to the circle. So, if we consider option C it is true in this case.

Since the acceleration vector is towards the center or along the radius of the circle, and the velocity vector is tangential to the circle, these two are perpendicular to each other. So, option D is also true. Therefore, the acceleration is not tangent to the circle.

Hence, Option A is the correct answer.

Note: If a particle is moving in a circle with a constant angular speed, then it performs uniform circular motion. In a uniform circular motion, the tangential acceleration of the particle is zero. The particle moves under radial acceleration only which points to the center of the circle.