The **rotational kinematics** relations allow to find the results for the questions about the **movement **of the **three people** on the **turntable** are:

** 1 and 2)** All **periods** are **equal**, T₂ = T and T₃ = T.

**3) **The** linear velocity** of the 2nd person is: v₂ =

**4)** The **linear velocity** of the 3rd person is: v₃ = ½ v

**5) **The **linear acceleration **of the 2nd person is: a₂ =

** 6)** The** linear acceleration** of the 3rd person: a₃ = ½ a

**Rotational kinematics **studies the** rotational motion** of bodies looking for relationships between **angular position**, **angular velocity**, and **angular acceleration.**

In the case where the **angular accleration** is **zero**, the expression for the **velocity **is:

Where w is the angular velocity and Δw and Δt are the variation in angle t over time.

**1 and 2)**

Indicates that people are on a turntable, the **period** is when we have a **complete rotation** θ = 2π rad in time, therefore the **period** and the **angular** **velocity** are related.

In the apparatus of parks the** angular velocity** is **constant** and we see that it does **not depend** on the **radius**, therefore the** period** for **all **the **people** is the** same.**

T = T₁ = T₂

**3)** They indicate that the **speed** of the** 1 person **who is in the position r=R on the plate is v, let's calculate the **speed** for the **2 person** who is in the position r =

**Linear** and **angular** variables are **related**.

v = w r

Let's substitute for the **1st person**.

v = w R

For the **2nd person**.

v₂= w ( )

We **solve** these two equations.

**4) **We carry out the same calculation for the **3rd person.**

v₃ = w ½ R

We** solve **the two equations.

v₃ = ½ v

**5) **Ask for **radial acceleration.**

The relationship between radial and angular acceleration is.

a = α R

We substitute for the **1st person**.

a = α R

For the **second person**.

a₂ = α ( )

We solve the two equations

a₂ =

**6)** Ask the radial acceleration of the **3rd person**.

We substitute.

a₃ = α (½ R)

We solve.

a₃ = ½ a

In conclusion, using the **rotational kinematics **relations we can find the results for the questions about the **movement** of the **three people** on the **turntable **are

** 1 and 2)** All **periods** are **equal**, T₂ = T and T₃ = T.

**3) **The** linear velocity** of the 2nd person is: v₂ =

**4)** The **linear velocity** of the 3rd person is: v₃ = ½ v

**5) **The **linear acceleration **of the 2nd person is: a₂ =

** 6)** The** linear acceleration** of the 3rd person: a₃ = ½ a

Learn more about **rotational kinematics** here: brainly.com/question/14524058