Question

A 20g steel weight is placed on the edge of a 30cm diameter plastic disk. The coefficient of static friction between the steel weight and plastic disk is 0.4. At what angular velocity, ω will the weight slide off the disk? Your solution should include “known”, a pictorial representation, a physical representation and a free-body diagram. Hint: Apply Newton’s second law using v = rω, instead of v, as in the example.

Pictorial Representation

a. sketch showing important points in the motion

b. coordinate system

c. symbols for knowns and unknowns Known: Find:ωmax

2) Physical Representation

a. motion diagram

b. force identification

c. free-body diagram

3) Mathematical Representation

a. start with Newton’s first or second law

b. include other information as needed

c. solve!

2 nd law for r-axis 2 nd law for z axis

Answer 1

The weight will slide when the centripetal force is equal to the force of static friction:

$$ma=f,\\\space\\ a=v^2/r=(\omega r)^2/r=\omega^2r,\\$$

$$m\omega^2r=\mu mg,\\\space\\ \omega=\sqrt{\frac{\mu g}r}=5.11\text{ rad/s}.$$