A ball with a mass of .5kg is attached to a 1m string. The string is attached to a post and is free to rotate. The string can be assumed to be weightless and not stretch. The ball is spun around the post in the horizontal plane (so gravity is perpendicular to the string and direction of motion) at a rate of 2π radians per second and that is slowing down by .2 rad/s^2. What is the total acceleration vector and the tension in the string?
Simple harmonic motion
Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.
Simple Pendulum
A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.
Oscillation
In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.
A ball with a mass of .5kg is attached to a 1m string. The string is attached to a post and is free to rotate. The string can be assumed to be weightless and not stretch. The ball is spun around the post in the horizontal plane (so gravity is perpendicular to the string and direction of motion) at a rate of 2π radians per second and that is slowing down by .2 rad/s^2. What is the total acceleration vector and the tension in the string?
Write the given values using a suitable variable.
Here m signifies ball mass, l signifies string length, w signifies initial angular speed, and a signifies angular acceleration. Determine the normal acceleration using the given expression.
Find an using the given expression and values above.
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