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Let's learn circular motion Part 1
Let's calculate the tension in the string at the top of the circle. Notice that both of the forces T and mg are directed downwards towards the center. Since our block is in circular motion, we know that the NET FORCE must act towards the center of the circle.
That is, the NET FORCE towards the center, or the centripetal force, is the resultant or SUM of these two REAL forces. You should never label Fc in a freebody diagram!
net force to the center = T + mg
Fc = T + mg
m(v2/r) = T + mg
T = m(v2/r) - mg
If we wanted to calculate the minimum or critical velocity needed for the block to just be able to pass through the top of the circle without the rope sagging then we would start by letting the tension in the rope approaches zero.
0 = m(v2/r) - mg
m(v2/r) = mg
v2/r = g
v2 = rg
v = v(rg)
Now let's calculate the tension in the string at the bottom of the circle. Since the block is maintaining a circular path, we take the direction towards the center as positive. The NET FORCE acting towards the center, Fc, is the resultant force or the difference between T and mg since they now point in opposite directions.
net force to the center = T - mg
Fc = T - mg
m(v2/r) = T - mg
T = m(v2/r) + mg
This formula will be used frequently to calculate the tension in the string in a simple pendulum as the pendulum bob swung through its lowest position - the equilibrium position, the point of greatest KE.
Let's learn circular motion Part 1
Uniform Circular Motion
Definition- "The motion of the particle along a circumference of a circle with constant speed. "
OR
"Periodic Motion of a particle moving along a circumference of a circle with constant angular speed"
Examples :
- Motion of earth and other planets around the sun.
- Motion of tip of the minute hand, hour & secondhand of the clock
Period (T) & Frequency (n)
Definition: "The time taken by a particle performing uniform circular motion to complete one revolution is called as a periodic time."
OR
"The time taken by a particle performing uniform circular motion to travel a distance equal to circumference of circle is called as periodic time."
Formula
Period = Circumference of circle
Linear Velocity(v)
T = 2πr
v
But, v= rω
T= 2π
ω
S.I. unit of period is Second
Frequency
Definition- "The number of revolution performed by particle performing uniform circular motion in unit time"
The frequency of revolution is reciprocal of the period
n = 1 = ω = v
T 2π 2πr
S.I. unit of frequency is hertz (Hz)
Vertical circular motion
Top of the circle:
Let's calculate the tension in the string at the top of the circle. Notice that both of the forces T and mg are directed downwards towards the center. Since our block is in circular motion, we know that the NET FORCE must act towards the center of the circle.
That is, the NET FORCE towards the center, or the centripetal force, is the resultant or SUM of these two REAL forces. You should never label Fc in a freebody diagram!
net force to the center = T + mg
Fc = T + mg
m(v2/r) = T + mg
T = m(v2/r) - mg
If we wanted to calculate the minimum or critical velocity needed for the block to just be able to pass through the top of the circle without the rope sagging then we would start by letting the tension in the rope approaches zero.
0 = m(v2/r) - mg
m(v2/r) = mg
v2/r = g
v2 = rg
v = v(rg)
Bottom of the circle:
Now let's calculate the tension in the string at the bottom of the circle. Since the block is maintaining a circular path, we take the direction towards the center as positive. The NET FORCE acting towards the center, Fc, is the resultant force or the difference between T and mg since they now point in opposite directions.
net force to the center = T - mg
Fc = T - mg
m(v2/r) = T - mg
T = m(v2/r) + mg
This formula will be used frequently to calculate the tension in the string in a simple pendulum as the pendulum bob swung through its lowest position - the equilibrium position, the point of greatest KE.
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