Two skaters are performing on ice. One skater is gripping the other's hand and spinning her in an arc around his body. The distance between the skaters' grip and the outer edge of the arc is $3.0 \mathrm{~m}$. The skater is being swung around at $2.0 \mathrm{rpm}$ and has a mass of $54 \mathrm{~kg}$. Calculate the centripetal force.

A bucket of water is attached to a rope and is being swung around in a vertical circle. (a) What force is responsible for keeping the bucket moving in a circle? (b) Identify the source of the force in (a). (c) The water-filled bucket has a mass of $15 \mathrm{~kg}$ and is swinging at a velocity of $2 \mathrm{~m} / \mathrm{s}$ in a circle with a radius of $2 \mathrm{~m}$. Calculate the magnitude of the force.

A moon orbits a planet in a circular orbit so that its velocity along the circular path changes continuously with time. (a) Does the force of gravity act perpendicular or parallel to the moon's velocity? Explain. (b) Explain how the force of gravity changes the moon's velocity.

A space station is rotating at $12 \mathrm{~m} / \mathrm{s}$. The artificial gravity is equal to $50.0 \%$ of that found on Earth. What is the radius of the station?

Suppose that you have the vector displacement information for the two-dimensional motion of a train. (a) Explain how you would calculate the average velocity of the train. (b) Explain how you would calculate the average speed of the train.

Describe the method for algebraically determining the sum of two vectors.

A roller coaster car is at the lowest point on its track, where the radius of curvature is $20.0 \mathrm{~m}$. At this point, the apparent weight of a passenger on the roller coaster is $3.00$ times her true weight. What is the speed of the roller coaster?

A coin is resting on a vinyl record. The coin slips off the record when the rotation rate is $0.30 \mathrm{rps}$ (rotations per second). Determine the coefficient of static friction between the coin and the record. The radius of the record is $15 \mathrm{~cm}$.

A rock falls off a cliff on the Moon. (a) Identify how the motion of the rock differs from the motion of a rock falling from a cliff on Earth. (b) Identify how the motion of the rock is similar to the motion of a rock falling from a cliff on Earth.

You walk $1.3 \mathrm{~km}$ to the store and then return home. The entire trip takes $40.0 \mathrm{~min}$, ignoring the time spent shopping. (a) Determine your total displacement, and explain how you obtained this result. (b) Determine your average speed, in kilometres per hour, and explain how you obtained this result. (c) Determine your average velocity, in kilometres per hour, and explain how you obtained this result.

A top-loading washing machine with $2.0 \mathrm{~kg}$ of clothes inside is on spin cycle. The tub, with a radius of $0.35 \mathrm{~m}$, is rotating at $50.0 \mathrm{rpm}$. Determine the centripetal force acting on the clothes.

In a science fiction movie, a spacecraft has a rotating section to provide artificial gravity for the long voyage. A physicist watches a scene filmed from the interior of the spacecraft and notices that the diameter of the rotating section of the craft is about five times the height of an astronaut walking in that section (or about $10 \mathrm{~m}$ ). Later, in a scene showing the spacecraft from the exterior, she notices that the living quarters of the ship rotate with a period of about $30 \mathrm{~s}$. Did the movie get the physics right? Compare the centripetal acceleration of a $1.7 \mathrm{~m}$-tall astronaut at his feet to that at his head. Compare these accelerations to $g$.

The centripetal acceleration of an object at Earth's equator results from the daily rotation of Earth. Calculate the object's centripetal acceleration, given that the radius of Earth at the equator is $6.38 \times 10^6 \mathrm{~m}$.

Consider a banked curve on an exit ramp for a highway in the middle of winter when the road surface is covered with very slippery ice. (a) How does the banking angle of the road help drivers make it safely around the curve? What force (or component of force) is responsible? Explain your reasoning. (b) Explain why drivers must go much more slowly under these circumstances. (c) A student claims, "If banking angles help drivers safely navigate curved sections of road, why not make the banking angles significantly larger?" Identify one problem that might occur if this suggestion were used. Justify your answer.