- #1

TheDude710

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Any help would be great, thanks!

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- Thread starter TheDude710
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In summary, To find dx(t)/dt, we can use the equation d^2x/dt^2 = sin(x), where x is a function of time 't'. By letting a = dx/dt, we can simplify the equation to da/dt = sin(x). Then, by integrating both sides, we can solve for dx/dt and find the desired value.

- #1

TheDude710

- 14

- 0

Any help would be great, thanks!

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- #2

learningphysics

Homework Helper

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da/dt=d^2x/dt^2

Therefore

da/dt = sin(x)

(da/dx)(dx/dt) = sin(x)

(da/dx)(a) = sin(x)

a da = sin(x) dx

And you can get a by integrating both sides...

- #3

thepatientmental

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To solve this problem, we can use the chain rule of differentiation. Let's start by rewriting the given equation as:

d^2x/dt^2 = sin(x(t))

We can then apply the chain rule to find dx/dt:

d/dt(d^2x/dt^2) = d/dt(sin(x(t)))

By the chain rule, the left side becomes:

d^2x/dt^2 * dx/dt = cos(x(t)) * dx/dt

We can rearrange this to solve for dx/dt:

dx/dt = (d^2x/dt^2) / cos(x(t))

Substituting the given equation for d^2x/dt^2, we get:

dx/dt = sin(x(t)) / cos(x(t))

Finally, we can simplify this by using the trigonometric identity for tangent:

dx/dt = tan(x(t))

Therefore, x dot (dx/dt) is equal to tan(x(t)). I hope this helps you solve your rigid body rotation problem!

A rigid body rotation problem is a physics problem that involves finding the angular velocity, angular acceleration, or position of a rigid object rotating around a fixed axis. It typically involves using principles of rotational kinematics and dynamics.

To solve a rigid body rotation problem, you will need to use equations and principles from rotational kinematics and dynamics. This may involve finding the moment of inertia, applying Newton's laws of motion, and using conservation of angular momentum. It is important to clearly define the problem and draw diagrams to assist in the solution process.

"x dot" is a notation used to represent the angular velocity of a rigid body. It is typically represented by the symbol ω (omega) and is measured in radians per second. It is the rate of change of the angular displacement of the object over time.

Some common types of rigid body rotation problems include finding the angular velocity or acceleration of a rotating object, determining the torque needed to achieve a certain angular acceleration, and finding the final position or velocity of a rotating object after a certain amount of time.

Some tips for solving a rigid body rotation problem include clearly defining the problem, drawing diagrams to assist in visualization, using the correct equations and principles, and checking your answer to ensure it makes sense. It may also be helpful to practice solving similar problems to become more familiar with the process.

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