A car of mass 8000 kg moves in a circular path of radius 10 m with a linear velocity of 50 m/s. What is the angular velocity of the car?

1. Break Down the Problem

To find the angular velocity ($\omega$) of the car, we can relate linear velocity ($v$) to angular velocity through the formula: $\omega = \frac{v}{r}$ where:

• $v$ is the linear velocity,
• $r$ is the radius of the circular path.

2. Relevant Concepts

From the formula above:

• Given:
  • Mass of the car ($m$) = 8000 kg (not directly relevant to angular velocity)
  • Radius ($r$) = 10 m
  • Linear velocity ($v$) = 50 m/s

3. Analysis and Detail

Plugging the known values into the formula: $\omega = \frac{50 \, \text{m/s}}{10 \, \text{m}}$ Calculating this gives: $\omega = 5 \, \text{rad/s}$

4. Verify and Summarize

The calculation is straightforward and matches the units for angular velocity. The relationship between linear and angular velocity was used accurately.

Final Answer

The angular velocity of the car is $\omega = 5 \, \text{rad/s}$.