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Learning Introductory Physics with Activities

Paul J. Emigh, Rebecka Tumblin, Kathryn Hadley, Danielle Skinner

Section 11.6 Uniform Circular Motion

An object moving in a circle with a constant speed is said to undergo uniform circular motion. The acceleration of such an object is entirely centripetal; that is, the tangential acceleration (and therefore the angular acceleration) are both equal to 0. As a result, the centripetal acceleration may be used in combination with the Law of Motion to determine the net force acting on the object.

Exercises Activity - Turning Truck

You see a truck with known mass \(M\) driving along a flat road at a constant speed \(v_{truck}\text{.}\) The truck reaches a part of the road that follows a circular path with radius \(R\text{.}\)

1. Representation.

Sketch a free-body diagram for the truck. What force points in the same direction as the acceleration?
Tip.
The only object in contact with the truck is the ground, so (static) friction between the ground and the truck’s tires must point in the direction of the acceleration.

2. Calculation.

Suppose you also know the coefficient of static friction \(\mu_s\) between the ground and the truck’s tires. Find two possible expressions for the magnitude of the force of static friction on the truck. Which expression is more useful if you want to know the exact magnitude of the frictional force?
Solution.
The model for static friction tells you that \(F^{sf} \le \mu_s F^N\text{.}\) This would allow you to find the maximum value static friction can be, but it will not specify what it actually is. The Law of Motion, on the other hand, states that \(F_{net} = ma\text{,}\) and since friction is the only horizontal force and the acceleration is centripetal, this can be rewritten as \(F^{sf} = M\frac{v_{truck}^2}{R}\text{,}\) which tells you the force exactly!
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