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The acceleration of the box is \(0.2\) meters per second squared.What is the coefficient of kinetic friction on the stone?Solution: According to Newton's Second Law: $$ma = \frac - mg\mu_k$$ We need to solve for \(\mu_k\).
What can the maximum angular speed be for which the block does not slip?
###Introduction### The dynamics of circular motion refer to the theoretical aspects of forces in circular motion.
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.
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).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.Consider a wet roadway banked, where there is a coefficient of static friction of 0.40 and a coefficient of kinematic friction of 0.2 between the tires and the roadway.The radius of the curve is R=80m (a) if the banking angle is 30,what is the maximum speed the automobile can have before sliding up the banking?The system is whirled in a horizontal circular path.The maximum tension that the string can withstand is 400 N.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.Example 1: A spaceship of mass 5000 kilograms is floating in outer space in a uniform circle of radius 1000 meters at a constant speed of 2 meters per second. Solution: Use the equation for a centripetal force: $$F_R = \frac = \frac = \frac = 20 \; N$$ Example 2: A 0.05-kilogram frisbee is flying in a circular arc where the radius is 12 meters and the constant speed is 30 meters per second. Solution: Again just plug-and-chug: $$F_R = \frac = 3.75 \; N$$ ###Finding Other Values### Sometimes it is instead necessary to find other quantities besides the force, such as the radius of the circle formed or the speed of the object.This section explores problem-solving in uniform circular motion with these goals in mind.