A beetle whose mass is 2 g sits on a turntable at a distance of 12 cm from the center. The turntable is rotating at 33 rpm.

(a) What are its acceleration and the centripetal force on it?

a =______ m/s2

Fc=_____ N

(b) What is the interaction that provides the centripetal force? Select all that apply.

-the gravitational force
-the force of friction
-the force of the beetle on the turntable
-the concentration of the mind of the beetle

At 33 rpm, the angular velocity is

w = 33*2*pi/60 = 3.46 rad/s

a = R*w^2, where R = 0.12 m
a = 1.43 m/s^2
Fc = M*a

Friction of the bug on the turntable provides the centripetalo force

To calculate the acceleration and centripetal force on the beetle, we need to use the following formulas:

(a) Acceleration (a):
The formula for centripetal acceleration is given by:
a = (v²) / r
where,
v is the tangential velocity (circumference of the circle traversed per unit time)
r is the radius of the circle

First, let's convert the given rotation rate from rpm to rad/s:
33 rpm = 33 * (2π rad/1 min) * (1 min/60 s) = 34.55 rad/s

Next, let's calculate the tangential velocity (v):
The circumference of the circle traversed by the beetle is equal to the circumference of the turntable.
Circumference = 2π * r
Circumference = 2 * 3.14 * 0.12 m = 0.7544 m

Tangential velocity (v) = circumference / time = 0.7544 m / 1 s = 0.7544 m/s

Now we have all the required values to calculate the acceleration (a):
a = (v²) / r
a = (0.7544 m/s)² / 0.12 m
a ≈ 4.736 m/s²

Therefore, the acceleration of the beetle is approximately 4.736 m/s².

Centripetal Force (Fc):
The formula for centripetal force is given by:
Fc = m * a
where,
m is the mass of the beetle
a is the acceleration

Given that the mass of the beetle is 2 g (or 0.002 kg), we can now calculate the centripetal force:
Fc = 0.002 kg * 4.736 m/s²
Fc ≈ 0.00947 N

Therefore, the centripetal force on the beetle is approximately 0.00947 N.

(b) The interaction that provides the centripetal force is:

- The force of friction between the beetle and the turntable.

The gravitational force, force of the beetle on the turntable, and the concentration of the beetle's mind (an unrelated factor) do not provide the centripetal force in this case.