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## Circular Motion

The wheels on the bus go round and round, but can you name all the forces in a rotating reference frame? Learn to derive these and more through sheer force of reason in Circular Motion.

# Level 2

During their physics field trip to an amusement park, Tyler and Maria took a ride on the Whirligig, which has long swings spinning in circles at relatively high speeds. As part of their lab assignment, they estimated that the riders were making a full circle of radius $$6.5 \text{ m}$$ every $$5.8$$ seconds. Determine the approximate speed of the riders on the Whirligig.

A bike moves at a rate of $$\si{18\ \kilo\meter/\hour}$$. The rear tire has a diameter of $$\si{70\ \centi\meter}$$ and has a toothwheel of diameter $$\si{7\ \centi\meter}$$. The sprocket (the gear that's turned by the pedals) has diameter $$\si{20\ \centi\meter}$$. Both gears are connected by the chain and there is no slippage between the chain and either gear. Under these conditions, how many times do the pedals revolve per minute?

In this matter, assume $$\pi = 3$$.

The above shows a pendulum which is in uniform circular motion on a horizontal plane, hanging on a string from the ceiling. In the picture, $$mg$$ denotes the gravitational force, and $$T$$ denotes the tensile force of the string. Which of the following statements is correct in this connection? (Ignore air resistance and the mass of the string.)

a) The magnitude of the tensile force $$T$$ is greater than that of the gravitational force $$mg$$.

b) If we cut off the string right at this moment, then the pendulum will move as if it is thrown to the $$x$$ direction.

c) The direction of the net force acting on the pendulum is the $$y$$ direction.

Two clocks $$A$$ and $$B$$ of radii $$r$$ and $$R$$ respectively, with $$r<R$$, show the same time.

The tip of the minute hand of which clock will move with greater speed?

Dominic is the star discus thrower on South's varsity track and field team. In last year's regional competition, Dominic whirled the $$1.6\text{ kg}$$ discus in a circle with a radius of $$1.1\text{ m}$$, ultimately reaching a speed of $$52\text{ m/s}$$ before launch. Determine the net force acting upon the discus in the moments before launch.

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