A carousel with a radius of R = 3.0 meters is initially at rest. It is then given a constant angular acceleration ? = 0.6 rad/s2 . A. Sketch the physical situation and label your sketch with appropriate quantities from the problem statement. Make a table of known/given information and unknown/wanted information (this may involve reading the rest of the problem before starting). List any physical assumptions you will be making to solve the problem. B. What is the angular velocity of the carousel after t = 8 s? What is the linear velocity of a child located at 2.5 meters from the center of the carousel after t = 8.0 s? What is the tangential acceleration of the child at that time? What is the child’s radial acceleration at that time? C. Determine the magnitude and direction of the child’s total acceleration vector after 8 seconds. Add this vector to your diagram above and show the directions of the radial and tangential components. D. How many rotations does the carousel complete in the first 8 seconds? E. Assess the validity of your work in the following ways: 1. Check the physical units of your expressions in part B-D. What are the units of angle? What are the dimensions of angle? What is the difference? 2. Would you expect the child to have larger centripetal acceleration or tangential acceleration? Why? Explain the role of these accelerations in affecting the motion of the child. Do your answers support the argument?
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 carousel with a radius of R = 3.0 meters is initially at rest. It is then given a constant
A. Sketch the physical situation and label your sketch with appropriate quantities from the problem statement. Make a table of known/given information and unknown/wanted information (this may involve reading the rest of the problem before starting). List any physical assumptions you will be making to solve the problem.
B. What is the
C. Determine the magnitude and direction of the child’s total acceleration vector after 8 seconds. Add this vector to your diagram above and show the directions of the radial and tangential components.
D. How many rotations does the carousel complete in the first 8 seconds?
E. Assess the validity of your work in the following ways:
1. Check the physical units of your expressions in part B-D. What are the units of angle? What are the dimensions of angle? What is the difference?
2. Would you expect the child to have larger centripetal acceleration or tangential acceleration? Why? Explain the role of these accelerations in affecting the motion of the child. Do your answers support the argument?
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