I have two disks. I know that disk A has a mass per unit area σ given by σ = 5r2 and disk B has σ = 3r3. Each disk has radius 10cm. I have a slope at angle 45 degrees to the horizontal that is 2 m long. I time with a stop watch how long it takes the disks to roll down the slope without slipping. (Assuming that the disk’s 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 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?
Angular Momentum
The momentum of an object is given by multiplying its mass and velocity. Momentum is a property of any object that moves with mass. The only difference between angular momentum and linear momentum is that angular momentum deals with moving or spinning objects. A moving particle's linear momentum can be thought of as a measure of its linear motion. The force is proportional to the rate of change of linear momentum. Angular momentum is always directly proportional to mass. In rotational motion, the concept of angular momentum is often used. Since it is a conserved quantity—the total angular momentum of a closed system remains constant—it is a significant quantity in physics. To understand the concept of angular momentum first we need to understand a rigid body and its movement, a position vector that is used to specify the position of particles in space. A rigid body possesses motion it may be linear or rotational. Rotational motion plays important role in angular momentum.
Moment of a Force
The idea of moments is an important concept in physics. It arises from the fact that distance often plays an important part in the interaction of, or in determining the impact of forces on bodies. Moments are often described by their order [first, second, or higher order] based on the power to which the distance has to be raised to understand the phenomenon. Of particular note are the second-order moment of mass (Moment of Inertia) and moments of force.
I have two disks. I know that disk A has a mass per unit area σ given by σ = 5r2 and disk B has σ = 3r3.
Each disk has radius 10cm.
I have a slope at angle 45 degrees to the horizontal that is 2 m long.
I time with a stop watch how long it takes the disks to roll down the slope without slipping.
(Assuming that the disk’s 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 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?
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