Simple Harmonic Motion of a rolling ball

In summary, the problem asks for the x component of a ball's position on a circular track with a radius of 0.61 m and an angular speed of 1.3 rad/s in the counterclockwise direction. Using the equation x=Acos\theta, with A being the radius and \theta=\omegat, the x component of the ball's position at 2.6 s is incorrect due to not using radians. The correct x component can be found by substituting the given values into the equation.
  • #1
MozAngeles
101
0

Homework Statement



A ball rolls on a circular track of radius 0.61 m with a constant angular speed of 1.3 rad/s in the counterclockwise direction.
A. If the angular position of the ball at t= 0 is [tex]\theta[/tex]= 0, find the x component of the ball's position at the time 2.6 s. Let [tex]\theta[/tex]= 0 correspond to the positive x direction.
B. Find the x component of the ball's position at the time 5.0 s.
C.Find the x component of the ball's position at the time 7.5 s

Homework Equations



x=Acos[tex]\theta[/tex]
[tex]\theta[/tex]=[tex]\omega[/tex]t

The Attempt at a Solution


i used x=Acos[tex]\theta[/tex], using .61 the raduis for the A, amplitude, and the angular speed of the ball 1.3 ras/s for omega and the given times 2.6 it is not coming out right so i do not know what i am doing wrong.
 
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  • #2
never mind.. i wasn't using radians.
 

What is Simple Harmonic Motion?

Simple Harmonic Motion is a type of periodic motion where the restoring force is directly proportional to the displacement from equilibrium. This means that the object will oscillate back and forth around a central point with a constant period and amplitude.

How does a rolling ball exhibit Simple Harmonic Motion?

A rolling ball can exhibit Simple Harmonic Motion if it is rolling on a horizontal surface with no friction. In this case, the ball will roll back and forth in a straight line with a constant period and amplitude.

What factors affect the period and amplitude of Simple Harmonic Motion for a rolling ball?

The period and amplitude of Simple Harmonic Motion for a rolling ball are affected by the mass of the ball, the radius of the ball, the magnitude of the force applied, and the surface on which the ball is rolling.

How is Simple Harmonic Motion of a rolling ball different from that of a pendulum?

While both involve periodic motion, Simple Harmonic Motion of a rolling ball is linear, while a pendulum exhibits angular motion. Additionally, the restoring force for a rolling ball is the force of gravity, while a pendulum's restoring force is tension in the string or rod.

What are some real-world applications of Simple Harmonic Motion of a rolling ball?

Simple Harmonic Motion of a rolling ball can be seen in various systems, such as car suspension, clock pendulums, and even the movement of molecules in a gas. It is also used in engineering designs for shock absorbers and vibration isolation systems.

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