Prove the magnitude of the centripetal force required for a uniform circular motion

Because there are two formulas for acceleration.

In the direction of velocity is a=δv δt

In the tangential direction of velocity is a=v2 r

The acceleration of a uniform circular moving object is always perpendicular to the direction of velocity, so a=v2 r is substituted because v=r.

So f=ma=mr

f=mv²/r

v=r so f=mr

Because f=ma=mr

So r = a

2.The direction of the speed of uniform circular motion changes all the time.

So a uniform circular motion is a variable velocity motion.

Proof from Newton's second law:

a= lim(t->infinitesimus)[v*sin( *t) t]**1)v*sin( *t) is the velocity of a uniform circular motion in t time, where the direction is in the same direction as v at t-> infinity;

f=m*a **2）

f = m*lim(t->infinitesimal )[v*sin( *t) t]**3)v = r **4).

There are mathematical calculus formulas.

Get. f=mrω²

Uniform circular motion is variable speed motion, which means that the speed direction of uniform circular motion is different at each moment, so it is variable speed motion.

Uniform circular motion 1Linear velocity v=s t=2 r t 2Angular velocity = t=2 t=2 f 3

Centripetal acceleration a=v2 r= 2r=(2 t)2r 4Centripetal force f centr=mv2 r=m 2r=m(2 t)2r 5Cycle vs. frequency t=1 f 6

Angular velocity vs. linear velocity v= r 7Angular velocity vs. rotational speed =2 n (here frequency is the same as rotational speed in the same sense) 8Main physical quantities and units:

Arc length (s): m (m) angle ( ) radian (rad) frequency (f): hertz (hz) period (t):

Second(s) Rotational speed (n): r s radius (r): meters (m) linear velocity (v):

m s angular velocity ( ) rad s centripetal acceleration: m s2 Note: (1) The centripetal force can be provided by a specific force, or by the resultant force, or by the component force, and the direction is always perpendicular to the direction of velocity.

2) The centripetal force of an object moving in a circular motion with uniform velocity is equal to the resultant force, and the centripetal force only changes the direction of the velocity, not the magnitude of the velocity, so the kinetic energy of the object remains the same, but the momentum keeps changing.

The direction of the centripetal force of uniform circular motion is always directed towards the center of the circle, and the direction of centripetal acceleration from Newton's second law is also always directed towards the center of the circle

So the answer is: the center of the circle

If the centripetal force increases suddenly, decomposing the motion into centripetal and perpendicular to the centripetal direction, then the object will suddenly gain acceleration in the centripetal direction, so that it will be closer to the center. Acceleration is always centripetal, independent of the perpendicular direction, and does not cause a change in the motion in that direction. As it gets closer, the radius decreases, the centrifugal force becomes larger, first it starts to balance with the centripetal force, and then decelerates to the centripetal ocean velocity is 0, at this time the radius is smaller than before, the centrifugal force is greater than the centripetal force, so it begins to move away from the center and do centrifugal motion.

The relationship between centripetal force and centrifugal force here is like a weight on a spring, suddenly adding a weight to a weight on a weight that is stationary on the spring, as if the centrifugal force is suddenly increased here, it will accelerate downward, decelerate, and bounce back up at rest. If the motion perpendicular to the centripetal direction is not affected, then the motion is an elliptical trajectory.

It's like suddenly increasing the centrifugal force here, this sentence is wrong, it's the centripetal force.

If the centripetal force increases suddenly, decomposing the motion into centripetal and perpendicular to the centripetal direction, then the object will suddenly gain acceleration in the centripetal direction, so that it will be closer to the center. Acceleration is always centripetal, independent of the perpendicular direction, and does not cause a change in the motion in that direction. As it gets closer, the radius decreases, the centrifugal force becomes larger, first it starts to balance with the centripetal force, and then decelerates to the centripetal ocean velocity is 0, at this time the radius is smaller than before, the centrifugal force is greater than the centripetal force, so it begins to move away from the center and do centrifugal motion.

The relationship between centripetal force and centrifugal force here is like a weight on a spring, suddenly adding a weight to a weight on a weight that is stationary on the spring, as if the centrifugal force is suddenly increased here, it will accelerate downward, decelerate, and bounce back up at rest. If the motion perpendicular to the centripetal direction is not affected, then the motion is an elliptical trajectory.

It's like suddenly increasing the centrifugal force here, this sentence is wrong, it's the centripetal force.

If the centripetal force is increased and the circular motion is still done, then the radius decreases.

If the centripetal force suddenly increases during a uniform circular motion, the motion will accelerate towards the center and gradually get closer, and the speed will decrease as it gets closer to the center in the process. After a certain point, the moving body will begin to move farther and farther away from the center, and the speed will slowly increase until it will begin to decrease again after the farthest point and get closer to the center point. Finally, the trajectory is an ellipse with the center of centripetal force as the focus, and the potential energy and kinetic energy of the centripetal force are continuously converted into each other, and the total energy is conserved.

Such a form of motion is the one in which most planets move.

The particle falls to the center of the circle in a spiral-like manner, just as a satellite loses power.

Either the radius changes, or the angular velocity, linear velocity, and period of motion change, depending on the formula.

Just if the centripetal force increases, it will move centripetally.

Hello landlord, 1Since they all do uniform circular motion, whether the speed of the circular motion when the radius is larger and the radius is smaller is the same, and if the velocity is the same, then of course the centripetal force is small when the radius is large. It is not difficult to find that if the velocity is not the same, this is a wrong problem, and when the radius changes, it must not be able to do uniform circular motion. So you're blind.

2.Constant angular velocity, of course, is that the larger the radius, the greater the centripetal force. The formula is proportional. )fn=mw^2r

Since it is a constant velocity and circumferential, then the resultant external force is the centripetal force.

Centripetal force = (m*v 2) r, there are three influencing factors, in general, the mass m is constant, can not be discussed.

Then the greater the velocity, the smaller the radius, and the greater the centripetal force; The smaller the velocity, the larger the radius, and the smaller the centripetal force.

When the object is moving in a uniform circular motion, when the linear velocity is constant, the larger the radius, the smaller the centripetal force (f=mv 2 r);

When the angular velocity is constant, the larger the radius, the greater the centripetal force (f=m 2r).

The magnitude of the centripetal force depends on the velocity in addition to the radius, and the larger the radius at the same speed, the smaller the force.

f=mv^2/r

It is one thing to combine the combined force of all forces.

The external force of the uniform circular motion is the centripetal force, the external force of the object in circular motion is not necessarily directed to the center of the circle, the component force pointing to the center of the circle is the centripetal force, the component force along the tangent direction changes the magnitude of the velocity, the centripetal force only changes the direction, and the direction of the centripetal force is also constantly changing, but the magnitude is unchanged.

Centripetal force f=mv 2 r=mw 2r=mvw

To put it simply, it is inaccurate to say that the centripetal force is proportional to the square of the linear velocity and inversely proportional to the radius, but should be proportional to the wv.

As for B, it is even more outrageously wrong.

ab has a variable radius r d option r = v divided by omega and substituted m by v square ratio r to get m times v times omega.

A radius is ignored by you, b is the same thing c is unchanged in all formulas except for radius, and there is no d f=vw (you know).

f=mvw: According to this formula, it can be seen that both D and ABC are due to uncertainties.

A: The reason for the error, the radius does not say whether it is certain or not.

B: The reason for the error is not to say whether the radius is certain or not.

3. The centripetal force is required for the uniform circular motion of the object, which always points to the center of the circle, so the direction is constantly changing, and the centripetal force is not a constant force, so AD is wrong;

b. Since the centripetal force points to the center of the circle and is always perpendicular to the direction of linear velocity, its effect is only to change the direction of linear velocity, and will not change the magnitude of linear velocity, so b is correct;

c. The centripetal force is the resultant external force directed to the center of the circle required by the object to do uniform circular motion, so C is correct;

Therefore, I chose: BC