A ball is swung in a horizontal circle of centre O with a constant speed. What is the direction of its acceleration?

Step 1: Analyze the question A ball moves in a horizontal circle with constant speed. We need the direction of its acceleration.

Step 2: The concept Acceleration is the rate of change of velocity, and velocity has both magnitude (speed) and direction. Even when the speed is constant, the ball's direction keeps changing as it moves around the circle. So the velocity is changing, which means the ball is accelerating.

• The velocity always points along the tangent to the circle.
• The change in velocity (Δv) over a short time points toward the centre.
• This acceleration is called centripetal acceleration, and its magnitude is:

a = v²/r = ω²r

where v is the speed, r is the radius, and ω is the angular velocity.

Step 3: Why the other options fail

• A (Away from O): This is the direction of the "centrifugal" effect, which is not a real force acting on the ball. The real net force is inward.
• B (Along the circumference): The circumference is curved, and the direction of motion at any instant is along the tangent, not toward some point along the arc.
• D (Along a tangent): This is the direction of the velocity, not the acceleration. If there were tangential acceleration, the speed would be changing, but here the speed is constant, so the tangential component is zero.

Step 4: Answer The acceleration is directed toward the centre O.

Exam tip: Remember "Velocity is tangent, acceleration is centre." For uniform circular motion, the force and acceleration always point toward the centre (centripetal means "centre-seeking"). If you see "constant speed in a circle," think of an inward acceleration straight away.