a 0.12 kg is sitting on a record with a diameter of 0.30 meters. the record completes one turn on 0.40 seconds

Well, that 0.12 kg is really taking a spin on that record! It's like a tiny dancer on a giant stage. But don't worry, it won't break out any choreography. Dancing isn't really its forte, after all. Instead, the record completes one turn in 0.40 seconds, so the little 0.12 kg object will be twirling around at quite a speed! Just be careful, it might get a bit dizzy.

To solve this problem, we can use the formula for centripetal force:

Fc = (m * v^2) / r

Where:
- Fc is the centripetal force
- m is the mass of the object
- v is the velocity of the object
- r is the radius of the circular path

First, let's find the velocity of the object. Since the record completes one turn in 0.40 seconds, it means it completes a full revolution (360 degrees) in that time. So, we can calculate the angular speed (ω) as follows:

ω = 2π / T

Where:
- ω is the angular speed
- T is the time period

Let's calculate the angular speed:

ω = 2π / 0.40
ω = 15.7 rad/s

Now, we can find the linear speed (v) using the formula:

v = r * ω

Given that the record has a diameter of 0.30 meters, the radius (r) is half of that:

r = 0.30 / 2
r = 0.15 meters

Let's calculate the linear speed:

v = 0.15 * 15.7
v = 2.36 m/s approx.

Now, we can find the centripetal force (Fc):

Fc = (m * v^2) / r

Given that the mass (m) is 0.12 kg, we can substitute the values and solve for Fc:

Fc = (0.12 * 2.36^2) / 0.15
Fc = 0.27 N approx.

Therefore, the centripetal force acting on the object is approximately 0.27 N.

To find the speed at which the 0.12 kg object is moving on the record, we need to determine the circumference of the record and divide it by the time it takes to complete one turn.

Step 1: Find the circumference of the record.
The circumference of a circle can be found using the formula:

Circumference = π x diameter

Given that the diameter of the record is 0.30 meters, we can calculate the circumference:

Circumference = π x 0.30 m
Circumference ≈ 0.942 m

Step 2: Calculate the speed of the object.
Now that we know the circumference of the record, we can divide it by the time it takes to complete one turn to find the speed.

Speed = Circumference / Time

Given that the time for one turn is 0.40 seconds, we can calculate the speed:

Speed = 0.942 m / 0.40 s
Speed ≈ 2.355 m/s

Therefore, the 0.12 kg object is moving at a speed of approximately 2.355 m/s on the record.