A 200 g solid sphere of R= 25 cm radius and a 300 g solid cylinder of identical radius vithout slipping down a 30° slope, starting from a vertical height of 1.2 m. From the sli class, we know that the moment of inertia for a solid sphere rotating about its center i: 2/5)MR? and for a cylinder its lc = (1/2)MR². a) Calculate the linear acceleration of each as they roll down the slope. Hint: there two equations here: F = ma for motion parallel to the plane, where the force: the relevant component of gravity and the static friction of the plane acting on rim of the ball or cylinder, making it roll, and t = Ia, where the torque is provide that same static friction force. The linear acceleration a and the angular accelera a are related, in the case for rolling without slipping, by a = Ra. %3D b) Using conservation of energy, calculate for each of these objects their translati speed when they reach the hottom of theslone
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.
Step by step
Solved in 7 steps with 1 images
