The independence is due to the magnetic force of the Cyclotron,F=qvxB:
mv^2/r = qvB giving m/qB = r/v = T/2pi where T is the period.
When the radius of the circular motion is increased, the period of rotation also increases. This is because the period of rotation is directly proportional to the radius of the circle in uniform circular motion.
Period and frequency are inverses of each other. Period is the time it takes for one complete cycle of a wave, and frequency is the number of cycles of a wave that take place in a unit of time. Period is equal to one over the frequency, and frequency is equal to one over the period.
The relationship between the period of time and the velocity in circular motion is inverse. As the period of time increases, the velocity decreases, and vice versa. This is because velocity is defined as the distance traveled per unit of time, so if the same distance is covered in a longer period of time, the velocity will be lower.
Some sources of error in a uniform circular motion experiment could include inaccuracies in measuring the radius of the circle, variations in the centripetal force due to friction or air resistance, and inconsistencies in measuring the period of the motion. Additionally, human errors in timing the motion or setting the apparatus could also contribute to inaccuracies.
Period is independent from mass. Because period, or T = 1/f and f = cycles/time, then T = time/cycles.
When the radius of the circular motion is increased, the period of rotation also increases. This is because the period of rotation is directly proportional to the radius of the circle in uniform circular motion.
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Period and frequency are inverses of each other. Period is the time it takes for one complete cycle of a wave, and frequency is the number of cycles of a wave that take place in a unit of time. Period is equal to one over the frequency, and frequency is equal to one over the period.
The relationship between the period of time and the velocity in circular motion is inverse. As the period of time increases, the velocity decreases, and vice versa. This is because velocity is defined as the distance traveled per unit of time, so if the same distance is covered in a longer period of time, the velocity will be lower.
Some sources of error in a uniform circular motion experiment could include inaccuracies in measuring the radius of the circle, variations in the centripetal force due to friction or air resistance, and inconsistencies in measuring the period of the motion. Additionally, human errors in timing the motion or setting the apparatus could also contribute to inaccuracies.
Period is independent from mass. Because period, or T = 1/f and f = cycles/time, then T = time/cycles.
The period of a pendulum is (sort of) independent of the amplitude. This is technically true for very small, "infinitesimal" swings. In this range, amplitude does not affect period. For larger swings, however, a circular error is introduced, but it is possible to compensate with various designs. See the Related Link below for further information.
Some sources of error when performing a lab experiment on uniform circular motion include friction in the rotational system, inaccuracies in measuring the radius of the circle, errors in timing the period of rotation, and uncertainties in recording the angular velocity of the object. These errors can lead to discrepancies in calculated values for centripetal force, acceleration, or velocity.
In circular motion the centripetal force is proportional to the speed squared. The speed is the circumference divided by the period. So if the period is increased the speed will decrease and the centripetal force will decrease. For example if the period is doubled then the speed is reduced by one half and the speed squared is reduced by one quarter, and so the centripetal force is reduced by one quarter.
The time period of a simple pendulum depends only on the length of the pendulum and the acceleration due to gravity, not the mass of the pendulum bob. This is because the mass cancels out in the equation for the time period, leaving only the factors that affect the motion of the pendulum.
by using the formula we will calculat time period of simple harmonic motion
The period is independent of the mass.