a) What is the angular velocity of the system after the collision? b) How much kinetic energy is lost in the collision? c) If the angular position of the Cylinder varies as θ(t)=3.2t-t^2 find the centripetal acceleration of the red object (bead).
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 0.02 kg mass red object (bead) is moving at a speed of 10.0 m/s when it sticks to the edge
of a uniform solid cylinder. The cylinder is free to rotate about its axis through its center and has
a mass of 0.5 kg , a radius of 0.25 m and is initially at rest. I = 1/2MR2^2
a) What is the
b) How much kinetic energy is lost in the collision?
c) If the angular position of the Cylinder varies as θ(t)=3.2t-t^2 find the centripetal acceleration of the red object (bead).
d) A cord is now wrapped around the cylinder. Use the work energy theorem to find the angular velocity of the cylinder after 5.0m of cord have been removed by a 40N Force.
e) If the 40N force on the cord is replaced by a 40-N weight, what is the angular velocity of the cylinder after 5.0m of cord has unwound?
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 11 images
