A solid cylinder (disk) and a hollow cylinder are rolling with the same center- of-mass velocity v = 2 m/s on a level surface towards an incline. Both R cylinders have the same radius R and mass M. The moments of inertia are: 1 Solid cylinder I, MR? Hollow cylinder I, = MR² 2 (a) What is true about the kinetic energy when the cylinders are rolling on level ground? (i) they have the same translational kinetic energy (ii) they have the same rotational kinetic energy (iii) they have the same total kinetic energy [1] only (i) [2] only (ii) [3] (i) and (ii) [4] (i) and (iii) [5] (i), (ii), and (iii)
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.
![A solid cylinder (disk) and a hollow
cylinder are rolling with the same center-
of-mass velocity v = 2 m/s on a level
surface towards an incline. Both
R
cylinders have the same radius R and
mass M. The moments of inertia are:
1
Solid cylinder 1,
MR²
Hollow cylinder I, = MR²
(a) What is true about the kinetic energy when the cylinders are rolling on level ground?
(i) they have the same translational kinetic energy
(ii) they have the same rotational kinetic energy
(iii) they have the same total kinetic energy
[1] only (i) [2] only (ii) [3] (i) and (ii) [4] (i) and (iii) [5] (i), (ii), and (iii)
(b) Which conservation law will allow you to calculate the final height? Conservation of:
[1] momentum
[5] moment of inertia
[2] mechanical energy
[3] kinetic energy [4] angular momentum
(c) Calculate the maximum height the solid cylinder will reach before it rolls down again; please
use g = 10 m/s².
(d) Calculate the maximum height the hollow cylinder will reach before it rolls down again.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2b2ded1c-edab-4d29-8970-7423f6bcac66%2Ff3330a3d-88a0-44f1-b5ce-a9ab2b517109%2Fblxt6nt_processed.png&w=3840&q=75)
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