Angular accelaration problem help

[alexito01]

A penny rests on a record at a radius r=0.200m. The record player is turned on and the record steadily accelerates with angular acceleration alpha=20.0 rad/s^2. The coefficient of static friction between the record and the penny is 0.500. At what time will the penny begin to slip?

 

[arpanroy]

Basically the penny will begin to slip when the centrifugal force is greater than the frictional force.
Your frictional force is Umg where U is the coefficient of friction(0.5) in this case.
Ur centrifugal force will be mw^2r where w is the angular velocity.

solve for Umg=mw^2r first to get w at which it slips...

then use w=angular accel* t to get ur t

 

[baba89]

Based on the given information, we can use the equation for angular acceleration (alpha) to determine the angular velocity (omega) of the record player at any given time (t). This can be represented by the equation alpha = d(omega)/dt, where d(omega) represents the change in angular velocity over time (t).

Since we are interested in the time at which the penny will begin to slip, we can set up the equation for static friction (Ff = u*Fn) where Ff represents the force of friction, u represents the coefficient of static friction, and Fn represents the normal force (in this case, the weight of the penny). We can then equate this to the centripetal force (Fc = m*r*omega^2) where m represents the mass of the penny, r represents the radius, and omega represents the angular velocity.

Combining these equations, we can set up the following equation:

u*Fn = m*r*omega^2

We know that the weight of the penny (Fn) is equal to its mass (m) multiplied by the acceleration due to gravity (g). We also know the values for the coefficient of static friction (u), radius (r), and angular acceleration (alpha). Therefore, we can plug in these values and solve for the angular velocity (omega) at which the penny will begin to slip.

Once we have the angular velocity, we can use the equation omega = d(theta)/dt to determine the time (t) at which the penny will begin to slip. This can be done by rearranging the equation to solve for time (t), and then plugging in the values of omega and alpha.

In conclusion, using the given information and equations, we can determine the time at which the penny will begin to slip on the record player. It is important to note that this is assuming the record player is accelerating at a constant rate, and that there are no other external factors affecting the motion of the penny.