# Calculating velocity and angular velocity

Please help with the following problem. Provide step by step calculations fo reach.

A uniform cylinder (A) has a mass ( m = 3 kg ), radius ( r = 150 mm ), and can roll without sliding on a cart ( C ) of mass ( M = 5 kg ). Cylinder (A) is attached to a spring (AB) of stiffness (constant) k = 100 N/m as shown (attached). The system is released from rest when the spring is stretched ( = 20mm ). Neglecting wheel friction, determine the velocity of the cart and the angular velocity of the cylinder when the spring first reaches its undeformed state.

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#### Solution Preview

Let us assume, the angular velocity of the cylinder be, w, and the linear velocity of the Cart be, V.

Due to angular velocity of the cylinder, the linear velocity of the cylinder over cart, v = w*R

where R = radius of the cylinder = 150 mm = 0.15 m

mass of the cyliderm = 3 kg

Therefore, moment of inertia of the cylider about it's ...

#### Solution Summary

This solution is provided in 270 words. It uses moment of inertia and momentum law to find velocity, and then energy law to find angular velocity.