Group Problems #17 Physics 111-4 Spring 2012 Page 1 of 4
Group problem #17: rotational motion
On a lovely fall day, you decide to mow your lawn. To start a lawnmower, you must pull on the rope wound around the perimeter of a flywheel. After you pull the rope for 0.95 s, the flywheel is rotating at 4.5 rev/sec, at which point the mower is designed such that the rope disengages. This attempt at starting the lawnmower does not work and the flywheel slows, coming to rest 0.24 s after disengagement. Being frustrated, you start reading the operator’s manual. After reading the manual you decide to determine the average angular acceleration during spin up and the spin down. An angular speed of 3.5 rev/sec is required to start the mower. What is the maximum angular speed reached by the flywheel due to your effort? Should the mower have started?
Since you are interested in Astronomy, you decide to play with some numbers one quiet afternoon. Mars orbits the sun at a mean orbital radius of 228 Gm (1Gm = 109m) and has an orbital period of 687 days. Earth orbits the sun at a mean orbital radius of 149.6 Gm. You know that the Earth-Sun line sweeps out an angle of 360° during one earth year. You are wondering, approximately what angle is wept out by the Mars-Sun line during one Earth year? And along those same lines, you are wondering how frequently are Mars and the Sun in opposition (on diametrically opposite sides of Earth)?
While sitting on a park bench people watching during summer vacation, you watch a cyclist accelerate uniformly from rest. After 8.0s, you notice that the wheels have rotated 3.0 full revolutions. Since you took Physics, and have no appointments, you decide to calculate the angular acceleration of the wheels and angular speed of the wheels at the end of the 8.0s. You watch the bicyclist travel down a park path for 1 minute, at which point he disappears from view. Since you are thinking about walking that path, you are wondering how far the wheels (and thus the bicycle) have traveled before disappearing from view. You estimate that the radius of the bicycle tire is 35cm.
Over summer vacation you are hired as a safety inspector for an amusement park. The park’s 12m Ferris wheel rotates once each 27 seconds. Your boss asks you to calculate the angular speed of the Farris wheel in radians per second. However, the report form asks for the linear speed and acceleration of a passenger on the Farris wheel. For completeness sake, you decide to calculate all three values.