Solved Uniform Circular Motion Problems Physics

You are driving along an empty straight road at a constant speed u.At some point you notice a tall wall at a distance D in front of you.

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Circular motion dynamics revolve around a few key formulas pertaining to forces and acceleration.

First, we have the formula for acceleration in uniform circular motion: $$a_R = \frac$$ However, we can multiple both sides of the equation by the mass of the object: $$ma_R = \frac$$ And by Newton's Second Law: $$F_R = \frac$$ Finally, sometimes an object will have an additional force being applied to it beyond the centerpointing force.

Solution: The fact that the speed, radius, and acceleration are constant mean that the block is undergoing uniform circular motion.

There are two forces acting on the block on the plane of the ground: the centerpointing applied force on the block, and friction.

Usually this second force will be friction or gravity.

###Calculating Forces in Circular Motion### The equation $$F_R = \frac$$ is central to calculating forces pertaining to circular motion.

Would it require a larger force to (a) continue moving straight and decelerate to a full stop before the wall, or (b) turn left or right to avoid the wall?

(to make the calculation easier assume that the turn is done at a constant speed along a circular path).

Example 3: A block of mass \(2\) kilograms is sliding around in a circle at a constant speed of \(4\) meters per second.

If the coefficient of kinetic friction between the block and the ground is \(0.3\) and the constant acceleration of the block is \(10\) meters per second squared, find the radius of the circle formed by the block.


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