The circular motion and The centripetal acceleration | POINT classical mechanics
The circular motion and The centripetal acceleration
By studying Newton's second law, you learned that:
When a force acts on a moving object it gains acceleration (its velocity changes)The change in velocity depends on the direction of the net force acting relative to the direction of motion.
If the direction of the resultant force is:
1- In the same direction of movement
The velocity of the moving body increases.
The direction of movement of the body does not change
Example:
When the motorcycle driver increases the fuel consumption, it is affected by a force in the same direction of movement, increasing its speed.
2- Reverse the direction of movement
The velocity of the moving body decreases.
The direction of movement of the body does not change
Example:
When the motorcycle driver presses the brakes, the force is in the opposite direction of motion, so the speed decreases.
3- Perpendicular to the direction of movement
The velocity of a moving body remains constant.
The direction of movement of the body does changes
Example:
When the motorcycle driver leans his body to the right or left, a force is generated perpendicular to the direction of movement, so the direction of movement changes and he moves in a circular path.
*From the above it is clear that: In order for a body to move in a regular circular motion in a circular path, a resultant force of constant magnitude and perpendicular to the direction of its motion and in the direction of the center of the circle must continuously affect it. This force is called Centripetal force.
Regular circular motion
Motion of a body in a circular path with a constant speed and a changing direction
Centripetal force
A force that acts continuously in a direction perpendicular to the direction of motion of a body, changing its straight path into a circular path.
Centripetal Acceleration
When a net force F acts perpendicular to the direction of motion of a body of mass m and velocity v, it moves in a semi-circular path with a radius of r and is:
1- The speed (v) is constant along the circumference of the circular path.
2- The direction of velocity is constantly changing along the circumference of the circular path, and changing the direction of velocity means that the body acquires acceleration during its circular motion.The central wheel is called (a) and its direction is in Same direction as the centripetal force.
Centripetal acceleration:-
1- The speed (v) is constant along the circumference of the circular path.
2- The direction of velocity is constantly changing along the circumference of the circular path, and changing the direction of velocity means that the body acquires acceleration during its circular motion.The central wheel is called (a) and its direction is in Same direction as the centripetal force.
Centripetal acceleration:-
The acceleration acquired by a body in circular motion due to a change in the direction of velocity
If this body completes a full rotation in the same circular path
During a time T, which is called the period, the velocity (v) at which it moves is called the tangential speed, and is calculated from this equation: v = 2Ï€r/T
"Its direction is always in the direction of the tangent to the circular path"
If a body completes N complete revolutions in a given time t, then the time the periodicity of its movement is given by this equation: T = t/N
Periodic time:-
The time required to complete a complete cycle in a circular path.
Conclusion of the central acceleration (a)
If a body moves from point A to point B as shown in the figure, the speed (v) changes in direction but maintains its magnitude constant. Thus, the change in speed (Δv) results from a change in its direction only.
- From the similarity of the triangle (CAB) with the velocity triangle:
Δl/r = Δv/v
Δv = v.Δl/r
If the body moves from A to B during a period of time Δt, then:
a = Δv/Δt = (vΔl/Δt) . (1/r)
as v = Δl/Δt
a = v²/r
If an object moves with a tangential velocity v along the circumference r of a circle of radius r from point A to point B, covering a distance of ΔL and an angle of Δθ in
Calculate angular velocity:
If an object moves with a tangential velocity v along the circumference r of a circle of radius r from point A to point B, covering a distance of ΔL and an angle of Δθ in
time Δt, then the quantity is known as the (Δθ/Δt) angular velocity. (ω)
It is known that the value of the angle in radii is equal to the ratio of the arc length to the radius of the path.
Δθ = Δl/r
so ω = (Δl/r)/Δt = Δl/t × 1/r = v/r
so v = ωr
So, tangential velocity = angular velocity × radius
as v = 2Ï€r/T
so r= 2Ï€r/T
so = 2Ï€/T