2. We can use a simple model which uses ourunderstanding of uniform circular motion toestimate the largest possible rotational speed of aplanet around its own axis. For a planet of mass Mand radius R our model assumes that the planet"falls apart" when the loose rocks on the surface atthe equator are no longer sitting on the surfacebecause they leave the surface. A loose rock of massm is shown on the equator in the drawing.MmRС.Now return to the 'slowly' rotating planet (wherethe loose rocks are not flying off the surface) and consider aloose rock that is not on the equator, but at some higherlatitude, 0 (as shown). Do you need forces besides gravity andthe normal force to make this situation possible? Justify youranswer (you just need to justify whether you need anotherforce but not what that other force might be if it is needed).

Answered: Image /qna-images/answer/a5d93fe0-44eb-4fd5-82a3-c85e79d151c5.jpg

2. We can use a simple model which uses our understanding of uniform circular motion to estimate the largest possible rotational speed of a planet around its own axis. For a planet of mass M and radius R our model assumes that the planet "falls apart" when the loose rocks on the surface at the equator are no longer sitting on the surface because they leave the surface. A loose rock of mass m is shown on the equator in the drawing. M m. R Now return to the 'slowly' rotating planet (where the loose rocks are not flying off the surface) and consider a loose rock that is not on the equator, but at some higher latitude, 0 (as shown). Do you need forces besides gravity and the normal force to make this situation possible? Justify your answer (you just need to justify whether you need another force but not what that other force might be if it is needed). С. -------

2. We can use a simple model which uses our understanding of uniform circular motion to estimate the largest possible rotational speed of a planet around its own axis. For a planet of mass M and radius R our model assumes that the planet "falls apart" when the loose rocks on the surface at the equator are no longer sitting on the surface because they leave the surface. A loose rock of mass m is shown on the equator in the drawing. M m. R Now return to the 'slowly' rotating planet (where the loose rocks are not flying off the surface) and consider a loose rock that is not on the equator, but at some higher latitude, 0 (as shown). Do you need forces besides gravity and the normal force to make this situation possible? Justify your answer (you just need to justify whether you need another force but not what that other force might be if it is needed). С. -------

College Physics

1st Edition

ISBN:9781938168000

Author:Paul Peter Urone, Roger Hinrichs

Publisher:Paul Peter Urone, Roger Hinrichs

Chapter6: Uniform Circular Motion And Gravitation

Section: Chapter Questions

Problem 16PE: Olympic ice skaters are able to spin at about 5 rev/s. (a) What is their angular velocity in radians...

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Olympic ice skaters are able to spin at about 5 rev/s. (a) What is their angular velocity in radians per second? (b) What is the centripetal acceleration of the skater's nose if it is 0.120 m from the axis of rotation? (c) An exceptional skater named Dick Button was able to spin much faster in the 1950s than anyone since—at about 9 rev/s. What was the centripetal acceleration of the tip of his nose, assuming it is at 0.120 m radius? (d) Comment on the magnitudes of the accelerations found. It is reputed that Button ruptured small blood vessels during his spins.
The tires on a new compact car have a diameter of 2.0 ft and are warranted for 60 000 miles, (a) Determine the angle (in radians) through (which one of these tires will rotate during the warranty period, (b) How many revolutions of the tire are equivalent to your answer in part (a)?
Human centrifuges are used to train military pilots and astronauts in preparation for high-g maneuvers. A trained, fit person wearing a g-suit can withstand accelerations up to about 9g (88.2 m/s2) without losing consciousness, (a) If a human centrifuge has a radius of 4.50 m, what angular speed results in a centripetal acceleration of 9g? (b) What linear speed would a person in the centrifuge have at this acceleration?
An athlete swings a 5.00-kg ball horizontally on the end of a rope. The ball moves in a circle of radius 0.800 m at an angular speed of 0.500 rev/s. What are (a) the tangential speed of the ball and (b) its centripetal acceleration? (c) If the maximum tension the rope can withstand before breaking is 100. N, what is the maximum tangential speed the ball can have?
At its peak, a tornado is 60.0 m in diameter and carries 500 km/h winds. What is its angular velocity in revolutions per second?
A disk rotates about an axis through its center. Point A is located on its rim and point B is located exactly halfway between the center and the rim. What is the ratio of (a) the angular velocity A to that of B and (b) the tangential velocity vA to that of vB?
Microwave ovens rotate at a rate of about 6 rev/min. What is this in revolutions per second? What is the angular velocity in radians per second?
(a) What is the period of rotation of Earth in seconds? (b) What is the angular velocity of Earth? (c) Given that Earth has a radius of 6.4106 m at its equator, what is the linear velocity at Earth's surface?
Suppose a piece of food is on the edge of a rotating microwave oven plate. Does it experience nonzero tangential acceleration, centripetal acceleration, or both when: (a) the plate starts to spin faster? (b) The plate rotates at constant angular velocity? (c) The plate slows to a halt?
An automobile with 0.260 m radius tires travels 80,000 km before wearing them out. How many revolutions do the tires make, neglecting any backing up and any change in radius due to wear?
The dung beetle is known as one of the strongest animals for its size, often forming balls of dung up to 10 times their own mass and rolling them to locations where they can be buried and stored as food. A typical dung ball formed by the species K. nigroaeneus has a radius of 2.00 cm and is rolled by the beetle at 6.25 cm/s. (a) What is the rolling balls angular speed? (b) How many full rotations are required if the beetle rolls the ball a distance of 1.00 m?
A large centrifuge, like the one shown in Figure 6.37(a), is used to expose aspiring astronauts to accelerations similar to those experienced in rocket launches and atmospheric reentries. (a) At what angular velocity is the centripetal acceleration 10 g if the rider is 15.0 m from the center of rotation? (b) The rider's cage hangs on a pivot at the end of the arm, allowing it to swing outward during rotation as shown in Figure 6.37(b). At what angle below the horizontal will the cage hang when the centripetal acceleration is 10 g? (Hint: The arm supplies centripetal force and supports the weight of the cage. Draw a free body diagram of the forces to see what the angle should be.) Figure 6.37 (a) NASA centrifuge used to subject trainees to accelerations similar to those experienced in rocket launches and reentries. (credit: NASA) (b) Rider in cage showing how the cage pivots outward during rotation. This allows the total force exerted on the rider by the cage to be along its axis at all times.