Rim Cylinder
October 15th, 2006
What constant force must be exerted on the rope to bring the?
1.) A 217 kg merry-go-round in the shape of a uniform, solid, horizontal disk of radius 1.9 m is set in motion by wrapping a rope about the rim of the disk and pulling on the rope.
What constant force must be exerted on the rope to bring the merry-go-round from rest to an angular speed of 0.671 rev/s in 1.88 s? Answer in units of N
2.) A horizontal 948 N merry-go-round of radius 1:71 m is started from rest by a constant horizontal force of 71.4 N applied tangentially to the merry-go-round. The acceleration of gravity is 9.8 m/s^2 . Assume it is a solid cylinder.
Find the kinetic energy of the merry-go-round after 2.9 s. Answer in units of J.
1)
First, figure out how much torque is required to accelerate the merry-go-round to the indicated speed in the given time:
torque = (moment of inertia) * (angular acceleration)
(angular acceleration) = (change in angular speed)/time
You’ll need to look up the formula for moment of inertia of a uniform, solid disk.
Once you get the torque, divide by the radius to get the force.
2) Similar ideas at play here. However, you must first convert the given weight into a mass. (Remember the equation for weight of an object, which involves g = 9.8 m/s^2)
You need to figure out the angular speed of the disk after 2.9 s. That, and the moment of inertia, can be used to calculate kinetic energy. Formulas should be in your textbook.
Hope this helps.
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