a yo-yo is spun from rest by pulling on the string with a constant tension of 2.0N. The radius of the inner rod on which the string is strung around is 0.50cm. the tension applied for 5.0seconds after which the yo-yo is observed to spin with an angular velocity of 15 rad/sec

a)from the information given above, what is the moment of inertia of the yo-yo

b) what is the total angle the yo-yo has traveled through in these 5.0 seconds

Now you press your finger against the outer rim of the yo-yo ( which has a radius of 4.0 cm) to bring it to a stop. You apply a constant force of 2.0N directed perpendicular to the rim of the yo-yo. The tension from part a) is no longer being applied to the yo-yo. The coefficient of kinetic friction between you finger and the edge of the yo-yo is 0.80.

c) how ling does it take for the yo-yo to come to a stop

To solve these questions, we'll need to use some concepts from rotational motion and friction.

a) To find the moment of inertia of the yo-yo, we can use the formula:

I = (1/2) * m * r^2

Where:
I = Moment of inertia
m = Mass of the yo-yo
r = Radius of the inner rod

From the given information, we have the tension applied to the yo-yo (2.0 N) and the angular velocity after 5.0 seconds (15 rad/sec). Using the formula for torque:

τ = I * α

Where:
τ = Torque
α = Angular acceleration

At the beginning, the yo-yo starts from rest, so the angular acceleration is given by:

α = τ / I

We know the tension (τ) and the radius of the inner rod (r), so we can substitute these values into the equation above and solve for I.

b) To find the total angle the yo-yo has traveled in 5.0 seconds, we can use the formula:

θ = ω₀ * t + (1/2) * α * t^2

Where:
θ = Angle traveled
ω₀ = Initial angular velocity (0 rad/sec)
t = Time
α = Angular acceleration

Using the given values of time (5.0 seconds) and the angular velocity after 5.0 seconds (15 rad/sec), we can substitute them into the equation above to find the angle traveled.

c) To find how long it takes for the yo-yo to come to a stop when you press your finger against the rim, we need to consider the torque due to friction. The torque caused by friction is equal to the force of friction multiplied by the radius of the yo-yo.

τ_f = f * r

Where:
τ_f = Torque due to friction
f = Force of friction
r = Radius of the yo-yo

Using the coefficient of kinetic friction (0.80) and the force applied (2.0 N), we can calculate the force of friction. Then, using the torque equation above, we can solve for the angular acceleration due to friction. Finally, we can apply the kinematic equation for rotational motion (ω = ω₀ + α * t) to find how long it takes for the yo-yo to come to a stop.

Please let me know if you would like a step-by-step calculation for each question, or if you have any further questions!