Circular Motion Physics Example 3

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Example 3

medium
A car travels around a circular track of radius 50 m at 20 m/s. Find the centripetal acceleration.

Solution

  1. 1
    Identify the known values: radius r=50r = 50 m, speed v=20v = 20 m/s.
  2. 2
    Apply the centripetal acceleration formula: ac=v2ra_c = \frac{v^2}{r}.
  3. 3
    Substitute and calculate: ac=(20)250=40050=8 m/s2a_c = \frac{(20)^2}{50} = \frac{400}{50} = 8 \text{ m/s}^2.

Answer

ac=8 m/s2a_c = 8 \text{ m/s}^2
Centripetal acceleration always points toward the centre of the circular path. It depends on the square of speed, so doubling the speed would quadruple the acceleration. At 8 m/s^2, this is close to the acceleration due to gravity (g≈9.8g \approx 9.8 m/s^2), meaning the car needs significant friction to maintain the turn.

About Circular Motion

Motion of an object along a circular path where the speed may be constant but the velocity is continuously changing direction, requiring a centripetal acceleration.

Learn more about Circular Motion →

More Circular Motion Examples

Example 1 easy

A car drives around a circular track of radius [formula] at a constant speed of [formula]. What is t

Example 2 medium

A satellite orbits Earth at a radius of [formula] with a period of [formula]. What is its orbital sp

Example 4 medium

A point on the rim of a bicycle wheel ([formula]) moves at [formula]. What is the period of rotation

Example 5 hard

A ball on a [formula] string is swung in a vertical circle. What minimum speed must it have at the t

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