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QPage 48-49: Q10.3: HC Verma: Concepts of Physics - Volume 1 Chapter-3 Rest and Motion Kinematics Page 48-49: Q10.3 Solution: Give example where the velocity is perpendicular to the acc...

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often assume that in any circular motion the velocity is perpendicular to the acceleration, but this is true only when the speed is constant. If the speed changes, a tangential component of acceleration appears, so the net acceleration is not perpendicular to the velocity. Always verify that the acceleration considered is the total acceleration, not just the centripetal part.

Give example where the velocity is perpendicular to the acc...


Step-by-Step Verified Solution

Classic Example 1: Uniform Circular Motion

  1. A particle moves in a circle at constant speed.
  2. At any instant:
  3. Velocity (v) = tangent to the circle (along the direction of motion).
  4. Acceleration (a) = radial (towards the center of the circle), also called centripetal acceleration.
  5. The tangent and the radius are always perpendicular to each other.
At every point on the circle: v is tangent, a is radial → They are perpendicular (90°).

Classic Example 2: A Car Taking a Turn at Constant Speed

  1. A car moves along a circular curve on a flat road at a steady speed.
  2. At any instant:
  3. Velocity = along the tangent (forward direction of the car).
  4. Acceleration = towards the center of the curve (centripetal, provided by friction).
  5. The forward direction and the direction towards the center are perpendicular.
Velocity is forward; acceleration is sideways (towards the center) → They are perpendicular.

Classic Example 3: A Satellite in a Circular Orbit

  1. A satellite orbits the Earth in a circular path at constant speed.
  2. At any instant:
  3. Velocity = tangential to the orbit (direction of motion).
  4. Acceleration = towards the center of the Earth (centripetal, due to gravity).
  5. These are perpendicular at all times.
Velocity is tangential; acceleration is radial (towards Earth) → They are perpendicular.

Classic Example 4: A Stone Tied to a String and Whirled in a Horizontal Circle

  1. A stone is whirled in a horizontal circle at constant speed.
  2. At any instant:
  3. Velocity = tangent to the circle.
  4. Acceleration = towards the center (provided by tension in the string).
  5. The tangent and the radius are perpendicular.
Velocity is along the string's perpendicular; acceleration is along the string → They are perpendicular.

Important Caveat: What if the speed is changing?

If the particle is speeding up or slowing down while moving in a circle, there is also a tangential component of acceleration (parallel to velocity). In that case:

  1. The net acceleration is the vector sum of:
  2. Centripetal (radial) component (perpendicular to velocity)
  3. Tangential component (parallel to velocity)
  4. The net acceleration is then not perpendicular to velocity—it is at some angle.

So the condition velocity perpendicular to acceleration holds strictly only when:

The acceleration has no component along the direction of motion — i.e., the speed is constant and only the direction changes.


All Questions in this Chapter

QP 49-50: Q1 QP 49-50: Q2 QP 49-50: Q3 QP 49-50: Q4 QP 49-50: Q5 QP 49-50: Q6 QP 49-50: Q7 QP 49-50: Q8 QP 49-50: Q9 QP 49-50: Q10 QP 49-50: Q11 QP 49-50: Q12 QP 49-50: Q13 QP 50-51: Q1 QP 50-51: Q2 QP 50-51: Q3 QP 50-51: Q4 QP 50-51: Q5 QP 50-51: Q6 QP 50-51: Q7 QP 50-51: Q8 QP 50-51: Q9 QP 50-51: Q10 QP 51-54: Q1 QP 51-54: Q2 QP 51-54: Q3.1 QP 51-54: Q3.2 QP 51-54: Q3.3 QP 51-54: Q3.4 QP 51-54: Q4.1 QP 51-54: Q4.2 QP 51-54: Q5 QP 51-54: Q6 QP 51-54: Q7 QP 51-54: Q8.1 QP 51-54: Q8.2 QP 51-54: Q8.3 QP 51-54: Q9.1 QP 51-54: Q9.2 QP 51-54: Q10 QP 51-54: Q11 QP 51-54: Q12 QP 51-54: Q13 QP 51-54: Q14 QP 51-54: Q15.1 QP 51-54: Q15.2 QP 51-54: Q15.3 QP 51-54: Q16 QP 51-54: Q17 QP 51-54: Q18.1 QP 51-54: Q18.2 QP 51-54: Q19 QP 51-54: Q20 QP 51-54: Q21 QP 51-54: Q22 QP 51-54: Q23.1 QP 51-54: Q23.2 QP 51-54: Q23.3 QP 51-54: Q24 QP 51-54: Q25.1 QP 51-54: Q25.2 QP 51-54: Q25.3 QP 51-54: Q26 QP 51-54: Q27 QP 51-54: Q28 QP 51-54: Q29 QP 51-54: Q30 QP 51-54: Q31 QP 51-54: Q32.1 QP 51-54: Q32.2 QP 51-54: Q32.3 QP 51-54: Q33.1 QP 51-54: Q33.2 QP 51-54: Q34 QP 51-54: Q35 QP 51-54: Q36 QP 51-54: Q37 QP 51-54: Q38 QP 51-54: Q39 QP 51-54: Q40 QP 51-54: Q41 QP 51-54: Q42 QP 51-54: Q43.1 QP 51-54: Q43.2 QP 51-54: Q44 QP 51-54: Q45 QP 51-54: Q46.1 QP 51-54: Q46.2 QP 51-54: Q47.1 QP 51-54: Q47.2 QP 51-54: Q48 QP 51-54: Q49.1 QP 51-54: Q49.2 QP 51-54: Q50 QP 51-54: Q51 QP 51-54: Q52 QPage 48-49: Q1 QPage 48-49: Q2 QPage 48-49: Q3 QPage 48-49: Q4 QPage 48-49: Q5 QPage 48-49: Q6 QPage 48-49: Q7 QPage 48-49: Q8 QPage 48-49: Q9 QPage 48-49: Q10.1 QPage 48-49: Q10.2 QPage 48-49: Q10.3 QPage 48-49: Q11 QPage 48-49: Q12 QPage 48-49: Q13 QPage 48-49: Q14

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