# Determine the angular velocity in rad/s and degrees/s

• physicsgal
In summary, the conversation is about determining the angular velocity in radians and degrees per second of a car towing a trailer with wheels of 40cm in diameter. The formula used is # of rotations per second = distance traveled in 1 second / circumference of wheels. The answer for part a is 35.4pi radians per second and 6,372 degrees per second. For part b, the car turns 5.0 radians and 288 degrees in 60 seconds. The conversation also briefly discusses the advantages of using radians instead of degrees in these types of questions.
physicsgal
i think i have part a right (but who knows). i don't know about part b. any help is appreciated!

## Homework Statement

1) a car is traveling at 80km/h, and is towing a trailer. the wheels of the trailer are 40cm in diameter.

a) determine the angular velocity in rad/s and degrees/s

radius = 40cm/2 = 20 cm
distance traveled in 1 hr = 80km = 8,000,000
1 hr = 3600s

distance traveled in 1s = 8,000,000/3600 = 2,222.222

#of rotation in 1s = 2222.222/20pi = 35.37

angular velocity = 35.27 x 2pi = 70.74pi rads

70.74pr x (180/pi) = 6,372 degrees per second

b) through what angle does the tire turn in 60s? state your answer in radians and degrees

for this one i could just go 35.37 x 60s = 2122.7
360degrees x .7 = 252degrees?

252degrees x (pi/180) rad = 4.4 rad

?

and then i have to explain why radians are better than degrees in these types of questions. i haven't the foggiest idea.

~Amy

Circumfrence is $\pi$ d, not $\pi$ r

thanks

so:

a) determine the angular velocity in rad/s and degrees/s

radius = 40cm/2 = 20 cm
distance traveled in 1 hr = 80km = 8,000,000
1 hr = 3600s

distance traveled in 1s = 8,000,000/3600 = 2,222.222

#of rotation in 1s = 2222.222/40pi = 17.7

angular velocity = 17.7 x 2pi = 35.4pi rads

35.4pi x (180/pi) = 6,372 degrees per second

b) through what angle does the tire turn in 60s? state your answer in radians and degrees

17.68 x 60s = 1060.8
360degrees x .8 = 288degrees?

288degrees x (pi/180) rad = 5.0 rad?

~Amy

## 1. What is angular velocity?

Angular velocity is the rate of change of angular displacement with respect to time. It is a measure of how quickly an object is rotating.

## 2. How is angular velocity measured?

Angular velocity is typically measured in units of radians per second (rad/s) or degrees per second (deg/s).

## 3. How do you calculate angular velocity?

Angular velocity can be calculated by dividing the change in angular displacement by the change in time. This can be represented by the equation ω = Δθ/Δt, where ω is angular velocity, Δθ is change in angular displacement, and Δt is change in time.

## 4. Why is angular velocity important?

Angular velocity plays a crucial role in understanding the motion and behavior of rotating objects. It is used in various fields such as physics, engineering, and astronomy.

## 5. How does angular velocity differ from linear velocity?

Angular velocity refers to the rate of change of angular displacement, while linear velocity refers to the rate of change of linear displacement. Angular velocity is measured in units of radians per second or degrees per second, while linear velocity is measured in units of meters per second.

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