A tire with a diameter of 100 cm rotates 20 times in 3 seconds.

a) determine the angular velocity
b) how far the tire has travelled?
c) what is the speed in km/h?

a) angular velocity = 20(2π)/3 radians per second

= 40π/3 rad/sec

b) one rotation = (2π)(50) cm = 100π cm
so 20 rotations would cover 20(100π) or 2000π cm

c) assuming you mean linear speed
speed = distance / time = 2000π/3 cm/sec
= (2000π/3)(3600)/(100000) km/h
= 24π km/h

( there are 100000cm in 1 km, and 3600 seconds in 1 hour)

angular velocity is radians/sec

20rev/3sec = 20/3 rev/sec = 40pi/3 rad/sec

Assuming that the tire rolls without slipping, it has gone 20*2pi*100 = 4000pi cm

4000pi cm/3sec = 4188.8cm/sec * 3600sec/hr * 1km/100000cm = 150.8km/hr

My bad. I missed where it said diameter, not radius.

Reiny has it right.

thank you!

mori?

To find the answers to these questions, we need to use some formulas from rotational kinematics and basic conversion calculations. Here's how we can solve them step by step:

a) To determine the angular velocity (ω), we can use the formula:

ω = θ / t

Where:
ω is the angular velocity
θ is the total angle rotated
t is the time taken

In this case, the tire rotates 20 times. Since one complete rotation is equal to 2π radians, the total angle rotated (θ) is 20 * 2π.

Now, we can substitute the values into the formula:

ω = (20 * 2π) / 3

Simplifying this equation gives us the angular velocity.

b) To find how far the tire has traveled, we can use the formula:

Distance = circumference * number of rotations

The circumference of a tire can be calculated using the formula:

Circumference = π * diameter

Substituting the given diameter of the tire (100 cm) into the circumference formula will give us the circumference of the tire. Multiplying this circumference by the number of rotations will yield the distance traveled.

c) To find the speed in km/h, we need to convert the distance traveled to kilometers and the time given to hours.

First, we need to convert the distance traveled from cm to km by dividing by 100,000 (since there are 100,000 cm in 1 km).

Then, we need to convert the time from seconds to hours by dividing by 3,600 (since there are 3,600 seconds in 1 hour).

Finally, we can calculate the speed by dividing the distance (in km) by the time (in hours).

By following these steps, we will be able to find the answers to each of the questions.