A vertical solid disk of uniform mass M = 7 kg and radius R = 0.5 m is pivoted from point O as shown in the figure below. A constant radial force of F = 117 N is applied where the angle ß = 36º. If x = 0.36 m, determine the angular acceleration of the disk in Sl units at the instant shown. Express your answer using two decimal places. Please use the convention: Clockwise (-), Counterclockwise (+) when expressing your answer. Hint 1: The moment of inertia of a uniform disk about an axis of rotation passing through the center of mass (CM) is ICM = MR²/2. 9.80 m/s². Hint 2: Don't forget the force of gravity!!! Take g = F o p I CM
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 vertical solid disk of uniform mass ?=7kgM=7kg and radius ?=0.5mR=0.5m is pivoted from point ?O as shown in the figure below. A constant radial force of ?=117NF=117N is applied where the angle ?=36?β=36o. If ?=0.36mx=0.36m, determine the
Hint 1: The moment of inertia of a uniform disk about an axis of rotation passing through the center of mass (CM) is ???=??2/2ICM=MR2/2.
Hint 2: Don't forget the force of gravity!!! Take ?=9.80m/s2g=9.80m/s2.
Step by step
Solved in 2 steps with 2 images
