Acoin rests 13.0 cm from the center of a turntable. the coefficient of static friction between the coin and turntable surface is 0.440. the turntable starts from rest at t = 0 and rotates with a constant angular acceleration of 0.840 rad/s2. (a) once the turntable starts to rotate, what force causes the centripetal acceleration when the coin is stationary relative to the turntable? under what condition does the coin begin to move relative to the turntable?

(a) The turn table velocity

(b) 6.86s

Step-by-step explanation:

(a) The velocity of the turntable would be the one causing centripetal acceleration on the coin and the equation for that is

Where is the angular acceleration and r = 13 cm = 0.13 m is the distance form table origin to the coin

There's also an inertia force causes by the turntable angular acceleration, this force would have its acceleration equal to:

This acceleration would be perpendicular to the centripetal acceleration. So the total acceleration acting on the coin is:

(b) The coins begins to move when its total acceleration force begin to wins its static friction force, which is generated by gravity

We can substitute in the known parameters ()

So the coin would start moving after 6.86s.

the answer is here: : )

:

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12