A large stone disk is viewed from above and is initially at rest as seen in the figure below. The disk has a mass of 120.0 kg and a radius of 2.100 m. A constant force of 40.0 N is applied tangent to the edge of the disk for 58.0 s, causing the disk to spin around the z axis. (a) Calculate the angular acceleration of the stone, finding both the direction and magnitude. (Express your answer in vector form. Substitute numeric values, do not use variables.) (b) What is the final angular velocity of the stone? (Express your answer in vector form. Substitute numeric values, do not use variables.) (c) Calculate the translational speed for a point on the edge of the stone after 58.0 s.
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 large stone disk is viewed from above and is initially at rest as seen in the figure below. The disk has a mass of 120.0 kg and a radius of 2.100 m. A constant force of 40.0 N is applied tangent to the edge of the disk for 58.0 s, causing the disk to spin around the z axis.
(b) What is the final
(c) Calculate the translational speed for a point on the edge of the stone after 58.0 s.
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