Table of Contents
- 1 Why is velocity squared in centripetal acceleration?
- 2 Why is direction of angular velocity perpendicular?
- 3 How is the angular velocity of a body moving along a circular path related to its linear speed?
- 4 Why does angular velocity have a direction?
- 5 Why is angular velocity along the axis of rotation?
- 6 Why is centripetal force directed towards the center?
- 7 What is the relationship between linear speed and angular speed?
- 8 Why is VX always assumed to be constant in projectile motion?
- 9 What is the expression for displacement velocity and acceleration in SHM?
Why is velocity squared in centripetal acceleration?
Why centripetal acceleration is equal to velocity squared divided by the radius. The object’s speed is constant, but the velocity changes because the direction of the object is constantly changing. Consider the velocity at two moments during the circular path.
Why is direction of angular velocity perpendicular?
Direction of angular velocity of a body is perpendicular to the plane of motion, because the velocity of the body is cross-product of angular velocity and the perpendicular distance between the axis of rotation of the body and the angular velocity vector.
For a body moving along a circular path,show that, Linear speed=Angular velocity × Radius of the circle.
Why is it velocity squared?
Conceptually, it is velocity^2 (in simple simple terms) because the faster an object gets, the deceleration necessary to bring back to origional velocity it is the square of that factor of increase.
What is the relationship between velocity squared and centripetal force?
Note that the centripetal force is proportional to the square of the velocity, implying that a doubling of speed will require four times the centripetal force to keep the motion in a circle.
Why does angular velocity have a direction?
The direction of the angular velocity is along the axis of rotation. For an object rotating clockwise, the angular velocity points away from you along the axis of rotation. For an object rotating counterclockwise, the angular velocity points toward you along the axis of rotation.
Why is angular velocity along the axis of rotation?
Why is centripetal force directed towards the center?
To keep it moving in a circular orbit we need to pull it ( the body) towards the centre. This force which is needed to keep it moving in a circular path, is the centripetal force. It produces an acceleration which is always directed towards the centre of the circular path.
Why is the centripetal force directed to the center?
Therefore, the acceleration must be towards the center and hence also the force. Your diagram conveys the point that if a circular motion is uniform i.e., the magnitude of velocity remains fixed while its direction changes, the motion must be due to a force solely directed towards the center.
What is the relationship between velocity and angular velocity?
The greater the rotation angle in a given amount of time, the greater the angular velocity. Angular velocity ω is analogous to linear velocity v. We can write the relationship between linear velocity and angular velocity in two different ways: v=rω or ω=v/r.
What is the relationship between linear speed and angular speed?
Explanation: Linear velocity v is equal to the angular speed ω times the radius from the center of motion R .
Why is VX always assumed to be constant in projectile motion?
In the study of projectile motion, assuming Vx as a constant value is done in order to greatly simplify the equations of motion. As others have point out, the basic assumption being made is that there is no force being applied to the projectile in the x-direction.
What is the expression for displacement velocity and acceleration in SHM?
The curve between displacement and velocity of a particle executing the simple harmonic motion is an ellipse. When ω = 1 then, the curve between v and x will be circular. Hence the expression for displacement, velocity and acceleration in linear simple harmonic motion are The system that executes SHM is called the harmonic oscillator.
How do you find the differential equation for simple harmonic motion?
Solutions of Differential Equations of SHM. The differential equation for the Simple harmonic motion has the following solutions: x=Asin left ( omega t+phi right) x = Asin(ωt +ϕ) (When the particle at Q at in figure (b) (any time t).
What is x component and Y component in physics?
The component that pushes right or left is called the x-component, and the part that pushes up or down is called the y-component. Force components and shadows Mathematically, the components act like shadows of the force vector on the coordinate axes. In the picture directly below we see a force vector on the (x, y) plane.