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The moment of inertia of the compound pulley about its center is I. A rope wound around the inner pulley of radius r is attached to a spring of stiffness k. A constant force Po acts on the rope wrapped around the outer pulley, the radius of which is R. The pulley is at rest with the spring undeformed at the moment when Po is applied. Find the angular velocity when Î¸ = 1t.

-kr^2T^2 + 2PRT rad/s^2

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04:16

Problem 3: The radius of the pulley is R = 100 mm and its moment of inertia is I = 0.1 kgmÂ². The mass m = 5 kg. The spring constant is k = 135 N/m. The system is released from rest with the spring unstretched. At the instant when the mass has fallen 0.2 m, draw the FBD of the system and kinetic diagram. b) Find the angular acceleration of the pulley. c) Find the tension in the rope between the mass and the pulley.

01:22

The moment of inertia of the pulley system is I = 1.70 kg*m^2. The pulley consists of two cylindrical spools firmly attached to each other. The radii of the two cylindrical spools are r = 50 cm and r2 = 20 cm, respectively. A mass m1 = 2 kg is attached by a light strong rope to the spool of radius r1, and a mass m2 = 1.8 kg is attached by a light strong rope to the spool of radius r2.

1) Determine the angular acceleration.2) Determine the tension in the rope attached to mass m1.3) Determine the tension in the rope attached to mass m2.

01:14

A string wrapped around the pulley is pulled with a constant downward force F of magnitude 50 N. The radius R and moment of inertia I of the pulley are 0.10 m and 2.5 x 10^-3 kgÂ·m^2, respectively. If the string does not slip, what is the angular velocity of the pulley after 1.0 m of string has unwound? Assume the pulley starts from rest.

02:43

A pulley having a rotational inertia of $1.14 \times 10^{-3} \mathrm{~kg} \cdot \mathrm{m}^{2}$ and a radius of $9.88 \mathrm{~cm}$ is acted on by a force, applied tangentially at its rim, that varies in time as $F=A t+B t^{2}$, where $A=0.496 \mathrm{~N} / \mathrm{s}$ and $B=0.305 \mathrm{~N} / \mathrm{s}^{2} .$ If the pulley was initiallyat rest, find its angular speed after $3.60 \mathrm{~s}$.

01:27

A fixed 0.15kg solid disk pulley with a radius of 0.075m isacted on by a net torque of 6.4 m N what is the angularacceleration of the pulley? The moment of inertia of the pulley in½ mr^2

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