Rotational Motion Examples:
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1 Rotational Motion Examples: 1. A 60. cm diameter wheel rotates through 50. rad. a. What distance will it move? b. How many times will the wheel rotate in this time? 2. A saw blade is spinning at rpm. a. What is its angular velocity? b. Through how many radians will it spin in 2.0 seconds? c. How fast are the blade tips moving if the blade has a 30. cm diameter? 3. A washing machine spin dries clothes. It starts spinning at 20. rad/s and slows down to 8.0 rad/s while turning through 500. revolutions. a. What is the angular acceleration? b. How much time does it take to slow down? 4. A rotating satellite has the same angular velocity as the earth. If the satellite is positioned 5.00 x 10 7 m from the center of the earth, what is its tangential velocity? 5. The Earth rotates once every day. What is the velocity of a person on its surface? 6. A fan blade is rotating counterclockwise. a. What is the angular velocity of the fan blade at 300. rpm? b. What is the angular displacement of the blade after 5.00 seconds? c. If it comes to rest in 8.00 s, what is the angular acceleration and how many revolutions would it make? 7. Calculate the linear speed of the tip of each hand on the following clock: 8. Staring from rest, an Apache helicopter s rotors undergo an angular acceleration of 0.75 rad/s 2. a. How fast will they be traveling in 60 seconds? b. How many radians have they rotated through? c. What is the linear velocity of the tip of the rotors (r = 7.3 m)?
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3 Circular Motion Examples: 9. A frictionless 3.0 kg cart rolls down an incline, and then loops the loop. From what minimum height, h, should the cart be released so that it does not fall off of the circular track? 10. A car travels at 25.0 m/s along a horizontal curve of radius 450. m. What minimum coefficient of friction is necessary between its tires and the road in order for the car not to skid? 11. Tarzan, of mass 85 kg, holds onto a horizontal vine of length 8.0 m that is attached to a tree and jumps off of a limb on the tree. What is the tension in the vine as Tarzan passes the lowest point of his circular path? 12. The diagram shows an object of mass 3.0 kg traveling in a circular path of radius 1.2 m while suspended by a piece of string of length 1.9 m. What is the centripetal force on the mass? 13. A kg ball is swung in a horizontal circle of radius 1.20 m with a period of 1.25 s. What is the centripetal force on the ball? 14. What is the magnitude of Earth s centripetal acceleration as it orbits the Sun? 15. An object of mass m is on a horizontal rotating platform. The mass is located 0.22 m from the axle and makes one revolution every 0.74 s. The frictional force needed to keep the mass from sliding is 13 N. What is the object s mass?
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5 Gravitation Examples: 16. A black hole exerts a 50. N gravitational force on a spaceship. The black hole is positioned 1.0 x m from the ship. What is the force that the black hole exerts on the ship when it moves ½ of that distance from the black hole? 17. Assume the free fall acceleration on the surface of Jupiter, the most massive planet in our solar system, is 6.47 m/s 2 (Actually 25 m/s 2 ). Determine the mass of Jupiter if the radius of Jupiter is taken to be 7.1 x 10 4 km. 18. Oliver, whose mass is 65 kg, and Olivia, whose mass is 45 kg, sit 2.0 m apart in their physics classroom. a. What is the force of gravitational attraction between Oliver and Olivia? b. Determine Oliver s acceleration towards Olivia if there was no friction. 19. Cavendish s historic experiment is set up as shown to determine the force between two identical sets of masses. What would be the net force of attraction between one set of masses? 20. A space shuttle orbits the earth at an altitude where the acceleration due to gravity is 8.70 m/s 2. What is the shuttle s speed at this altitude? 21. A planet of radius 7.0 x 10 7 m has a gravitational field strength of 68 N/kg at its surface. What is the period of a satellite orbiting this planet at a radius of 1.4 x 10 8 m (twice the planet s radius)? 22. A satellite orbits a planet of mass 4.0 x kg at a velocity of 5.8 x 10 3 m/s. What is the radius of this orbit? 23. What is the centripetal acceleration of the Moon in its orbit around the Earth? 24. A 450. kg pieces of space debris initially at rest falls from an altitude of 6.2 x 10 5 m above the Earth s surface. What is its kinetic energy just before impact with the surface? (Ignore air resistance) 25. A 2.0 x 10 3 kg satellite is in a circular orbit around the Earth. The satellite has a linear speed of 3.6 x 10 3 m/s at an orbital radius of 3.1 x 10 7 m. What is the total energy of this orbiting satellite?
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2. To study circular motion, two students use the hand-held device shown above, which consists of a rod on which a spring scale is attached.
1. A ball of mass M attached to a string of length L moves in a circle in a vertical plane as shown above. At the top of the circular path, the tension in the string is twice the weight of the ball. At