Calculating Kinetic Energy & Speed of a Thrown Yo-Yo: Physics Problem Help

[matt62010]

yo you physics problem, please help!

A yo-yo has a rotational inertia of 820 g·cm2 and a mass of 115 g. Its axle radius is 3.9 mm and its string is 120 cm long. The yo-yo is thrown so that its its initial speed down the string is 0.8 m/s.
(a) How long does the yo-yo take to reach the end of the string?
(b) As it reaches the end of the string, what is its total kinetic energy?
J
(c) As it reaches the end of the string, what is its translational speed?
m/s
(d) As it reaches the end of the string, what is its translational kinetic energy?
J
(e) As it reaches the end of the string, what is its rotational speed?
rad/s
(f) As it reaches the end of the string, what is its rotational kinetic energy?
J
Can someone please explain how to do this?

 

[rcgldr]

Assume the string is infinitely thin, doesn't stretch, and no slippage. Compute the energy gain from decrease in height and figure out how this increase is distributed between angular and linear energy.

 

[thomate1]

Sure, I'd be happy to explain how to solve this physics problem. First, let's define some terms and equations that we will need to use.

- Rotational inertia (I): This is a measure of an object's resistance to rotational motion and is calculated by multiplying the mass of the object by the square of its distance from the axis of rotation. In this case, the yo-yo's rotational inertia is given as 820 g·cm2.
- Mass (m): This is the amount of matter in an object, and is given as 115 g for the yo-yo in this problem.
- Axle radius (r): This is the distance from the center of the yo-yo's axle to its outer edge, and is given as 3.9 mm.
- String length (L): This is the length of the string that the yo-yo is thrown down, and is given as 120 cm.
- Initial speed (v0): This is the yo-yo's speed at the beginning of its motion, and is given as 0.8 m/s in this problem.
- Final speed (vf): This is the yo-yo's speed at the end of its motion, and is what we will be solving for in this problem.

Now, let's look at the equations we will use to solve this problem:

- Kinetic energy (KE): This is the energy an object possesses due to its motion and is calculated by multiplying the mass of the object by half of its speed squared. The equation for kinetic energy is KE = 1/2 * m * v^2.
- Rotational speed (ω): This is the angular velocity of an object, or how fast it is rotating, and is calculated by dividing the final speed by the radius of rotation. The equation for rotational speed is ω = vf / r.
- Translational speed (v): This is the linear velocity of an object, or how fast it is moving in a straight line, and is calculated by dividing the distance traveled by the time it takes to travel that distance. The equation for translational speed is v = L / t.

Now, let's solve the problem step by step:

(a) To determine how long it takes for the yo-yo to reach the end of the string, we can use the equation for translational speed. We know the length of the string (L = 120 cm = 1.2 m