Question

The drum of a laundry machine, which can be modeled as a cylinder with a radius of 32 cm, is spinning about its vertical axis with an unknown angular speed ω. A wallet in contact with the inside wall of the spinning drum moves with the drum without slipping. The coecient of static friction between the wallet and the surface of the drum is µs=0.45. The mass of the wallet is 210 grams. What is the minimum value the angular speed can have (ωmin) so that the wallet does not slip ?

Answer 1

Answer:

8.25 rad/s

Explanation:

From the question. the condition for no slipping is represented as:

F = mg

$\mu _ s N = mg$

However, the normal force N acting on the drum is represented as :

N = mrω²

Thus; we can say :

$\mu_s mr \omega^2 = mg$

$\omega^2 = \frac{g}{\mu_sr}$

$\omega= \sqrt{\frac{g}{\mu_sr} }$

Given that :

the radius of the modeled cylinder = 32 cm = 0.32 m

the coefficient of static friction between the wallet and the surface of the drum $\mu_s$ = 0.45

mass (m)  of the wallet = 210 grams.

Then:

$\omega= \sqrt{\frac{9.81 \ m/s^2 }{0.45\ * \ 0.32 \ m} }$

ω = 8.25 rad/s

Thus, the minimum value the angular speed can have (ωmin) so that the wallet does not slip = 8.25 rad/s