Rotation of a Rigid Object About a Fixed Axis

In summary, a small object with a mass of 4.00kg moves counterclockwise at a constant speed of 4.50m/s in a circle with a radius of 3.00m, centered at the origin. Starting at the point (3.00i+0j)m, it undergoes an angular displacement of 9.00rad. The position vector is (x,y), with θ=0 when the position vector is pointing along the positive x axis. The particle is located in quadrant II and makes an angle of 112.5° with the positive x axis. Its velocity is 4.50m/s in the counterclockwise direction, and its acceleration is directed towards the center
  • #1
Joyci116
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Homework Statement


A small object with mass 4.00kg moves counterclockwise with constant speed 4.50m/s in a circle of radius 3.00m centered at the origin. It starts at the point with position vector (3.00i+0j)m. Then it undergoes an angular displacement of 9.00rad. (a.) What it is position vector? Use unit-vector notation for all vector answers. (b.) In what quadrant is the particle located, and what angle does its position vector make with the positive x axis? (c.)What is its velocity? (d.)In what direction is it moving? Make a sketch of its position, velocity, and acceleration vectors. (e.) What is its acceleration? (f.) What total force is exerted on the object?

m=4.00kg
V=4.50m/s
r=3.00m

This is just a scary problem!


Homework Equations


I was told to break it down into the x and y components, but how do you know to do that?
V=x/t
To find the direction it is moving, we would use the right hand rule, right?
a=V/t
ƩF=ma


The Attempt at a Solution


I need to break it into x and y components, but I am lost on how to do that.
 
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  • #2
Essentially you are given a problem in mixed coordinates, the initial position is (x,y) but the parameters of the problem are polar coordinates (r,θ). I would suggest it will be simpler to solve the motion in the polar coordinates since the radius is fixed. You therefore need to define how your polar coordinates will look, for instants you could define that θ=0 when the position vector from the origin points along the x axis.

Then define your initial position vector, and follow the steps it gives you on how it moves.

The best thing you can do is draw a really nice diagram. This will solve most of the problems.
 

What is rotation of a rigid object about a fixed axis?

Rotation of a rigid object about a fixed axis is a type of motion in which an object rotates around a fixed point or line. This type of rotation is also known as circular motion.

What is the difference between rotation and translation?

Rotation is a type of motion in which an object moves around a fixed point or line, while translation is a type of motion in which an object moves from one location to another without any rotation. In other words, rotation involves movement along a circular path, while translation involves movement along a straight line.

What is angular velocity?

Angular velocity is a measurement of how quickly an object is rotating about an axis. It is usually represented by the symbol ω and is measured in radians per second (rad/s).

What is moment of inertia?

Moment of inertia is a measure of an object's resistance to changes in its rotational motion. It is represented by the symbol I and is dependent on both the mass and distribution of mass of the object.

How does the moment of inertia affect the rotation of a rigid object?

The moment of inertia affects the rotation of a rigid object by determining how much torque is needed to produce a certain angular acceleration. Objects with a larger moment of inertia require more torque to achieve the same amount of rotation, while objects with a smaller moment of inertia require less torque.

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