Use circular motion equations to relate a linear speed or centripetal acceleration to the rotational speed.
Mr. Chowder ties an eraser to a string and swings it in a circle with a radius of 0.977 meters. The eraser makes 112 revolutions in a minute. Determine its acceleration (in m/s/s).
Acceleration
m/s/s
Determine the acceleration (in m/s/s) of a rider on the Cajun Cliffhanger (a barrel ride at an amusement park) if the rider makes 7 revolutions around the 5.67-m diameter circle in 35.7 seconds.
As Tyrone drives down Lake Avenue, the back wheel of his car spins at a rate of 290 revolutions/minute. The radius of the wheel is 0.354 m. A thumb tack is lodged in the tread of the tire at its outermost edge.
Calculate the linear speed of the thumb tack.
Speed
m/s
Calculate the acceleration of the thumb tack.
During the spin cycle of a washing machine, the clothes stick to the outer wall of the barrel as it spins at a rate as high as 1780 revolutions per minute. The radius of the barrel is 25.2 cm.
Determine the speed of the clothes (in m/s) which are located on the wall of the spin barrel.
Determine the acceleration of the clothes.
A manufacturer of CD-ROM drives claims that the player can spin the disc as frequently as 1130 revolutions per minute.
If spinning at this rate, what is the speed of the outer row of data on the disc; this row is located 5.52 cm from the center of the disc?
What is the acceleration of the outer row of data?
American physicist Gerard K. O'Neill proposed the construction of large rotating space cylinders several miles in length and several miles in diameter that could be used to colonize space. Inhabitants of the colonies would live inside the cylinders and be plastered to its surface due to inertial effects, thus creating a feel of being pulled downward towards the surface. Calculate rotation rate in revolutions per hour that a 5.00 miles in diameter cylinder must have to produce an acceleration of 9.8 m/s/s. Given: 1609 m = 1 mile.
Rotation Rate
rev/hr
Avery plays the young David in his church's play on David and Goliath. Avery is practicing with his 0.691-m long sling and finds that he can rotate it in a circle at 8.33 revolutions/second. But if he increases the length to 0.963 m, he is able to rotate at a less impressive 5.56 revolutions/second.
Calculate the acceleration of the sling when swung at 8.33 rev/s.
Calculate the acceleration of the sling when swung at 5.56 rev/s.