# Rotational Dynamics - sphere,block,pulley

1. Nov 11, 2005

### nyyfan0729

A solid sphere (I=(2/5)MR^2) with a radius R=0.10m is attatched to a massless rope by a frictionless axle that passes through the center of the sphere. The rope passes over an ideal pulley and is connected to a 1kg block. The sphere has a mass of 2kg. The surface has a meu that cannot equal 0. Assume that the ball always rolls without slipping and that the system is released from rest.
Calculate:
a. the acceleration of the system
b. the tension in the rope
c. the speed of the 1kg mass, by energy methods, after it has descended 0.25m.

2. Nov 11, 2005

### Fermat

Finding the acceleration is a little bit involved.

There is a small amount of (unknown) friction acting on the sphere, call it R.
Now use newton's 2nd law to get an expression, involving R, for the (linear) acceleration, a, of the sphere/block mass system.

The small amount of friction is what makes the sphere rotate as it moves along the table (?) surface.
Since this friction force rotates the sphere, then what is the angular acceleration of the sphere ?

If any object is rolling along a surface with a linear speed of v m/s, then what is the relationship between that speed and the object's angular velocity, ω ?

Similarly, what is the relationship between an objects linear acceleration, a, and its angular acceleration, α ?

You should now have three eqns invloving three unknown, R, a and α.