1. I have two disks. Disk A has a mass per unit area σ given by σ = 5r2 and disk B has σ = 3r3 Each disk has a radius of 10cm. I have a slope at angle 45 degrees to the horizontal that is 2 m long. I time with a stopwatch how long it takes the disks to roll down the slope without slipping. (Assuming that the disks are let go with zero velocity at the top of the slope). a) Calculate the mass of each disk. b) Calculate the moment of inertia of each disk. c) Calculate the acceleration down the slope for both disks. d) Calculate the time it takes for each disk to roll. e) What is the total kinetic energy for each disk at the end of the slope? f) At the end of the slope, a fly on the very edge of disk A walks towards the center of the disk at a speed of 1cm/s. What Coriolis acceleration is felt by the fly as it sets off?
Simple harmonic motion
Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.
Simple Pendulum
A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.
Oscillation
In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.
1.
I have two disks. Disk A has a mass per unit area σ given by σ = 5r2 and
disk B has σ = 3r3
Each disk has a radius of 10cm.
I have a slope at angle 45 degrees to the horizontal that is 2 m long.
I time with a stopwatch how long it takes the disks to roll down the slope without
slipping. (Assuming that the disks are let go with zero velocity at the top of the slope).
a) Calculate the mass of each disk.
b) Calculate the moment of inertia of each disk.
c) Calculate the acceleration down the slope for both disks.
d) Calculate the time it takes for each disk to roll.
e) What is the total kinetic energy for each disk at the end of the slope?
f) At the end of the slope, a fly on the very edge of disk A walks towards the center of
the disk at a speed of 1cm/s. What Coriolis acceleration is felt by the fly as it sets off?
Ignore parts a,b,c
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