levo

Further Mechanics

Centripetal acceleration

  • 1 thing to know
  • Papers 1 and 3

Overview

Recall questions on why circular motion at constant speed is accelerated, the direction of the acceleration, the two equations, and how each responds to a change of speed or radius.

What you need to know

Answer each one before you reveal it.

Your recallNot started
Numbers

Why is an object moving in a circle at constant speed accelerating, in which direction, and what happens if its speed doubles?

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    Why is an object moving in a circle at constant speed still accelerating?

    Model answer

    Velocity is a vector and its direction changes continuously, so the velocity is changing and there must be an acceleration.

  2. 2

    In which direction does centripetal acceleration act?

    Model answer

    It acts towards the centre of the circular path, at right angles to the instantaneous velocity.

  3. 3

    How does a vector diagram of the velocities at two nearby points lead to the equation for centripetal acceleration?

    Model answer

    The two velocity vectors, equal in magnitude v and separated by a small angle Δθ, form an isosceles triangle in which the change of velocity has magnitude Δv = vΔθ; dividing by Δt gives a = v(Δθ/Δt) = vω, and substituting v = ωr gives a = v²/r.

  4. 4

    In a vector diagram of the velocities at two nearby points on a circular path, why does the change in velocity point towards the centre of the circle?

    Model answer

    For a very small angle the vector difference between the two velocities lies almost perpendicular to both of them, which is along the radius directed inwards.

  5. 5

    State the two equations for centripetal acceleration:

    Model answer

    The centripetal acceleration is a = v²/r and equivalently a = rω².

  6. 6

    How can the two expressions for centripetal acceleration be shown to be equivalent?

    Model answer

    Substituting v = ωr into v²/r gives (ωr)²/r = ω²r²/r = rω².

Other ways to work this

The same content, four other ways.

What is inside Levo

Six ways to work the same material.

1Closed book
2Open book
3Closed book

The 3-step method, run for you

Answer cold, learn it, then prove it stuck. Levo tracks the jump between your first attempt and your last.

Working as a Physicist
Mechanics
Electric Circuits
Materials

Cram a whole paper in one sitting

Sort every topic into what you know and what you do not, then drill only the weak ones.

The gradient gives the .
accelerationvelocitydisplacement

Blank Blitz makes facts automatic

Rapid timed gap-fills on the terms and numbers you need to recall without thinking.

AThe equation is s = (u + v)t/2.
BThe equation is v = u + at.
CThe equation is s = ut + ½at².

Build It gets the exam shape right

Assemble a full-mark answer from its marking points, in the order an examiner wants them.

Speed means rate of change of distance.
TrueFalse

Test It catches misconceptions

Spot the fault in a statement. The traps are the mistakes students actually make.

721941163128510

Brain Breaks between sessions

Short focus games to reset attention, so the next set lands better than the last.

Every question in Further Mechanics, on a schedule.

Attempt a question from memory, write the correct version, then attempt it again. Levo records the jump between your first attempt and your last, and brings each question back on the day you are due to forget it.

Or £46 a year, about £3.83 a month. Cancel anytime.