A dragster is speeding down the track at 150m/s. its rear wheels are 2m in diameter, and its front wheels are 40cm in diameter. What are the angular velocities of the front and rear wheels, respectively?
To find the angular velocities of the front and rear wheels of the dragster, we need to use the relationship between linear velocity and angular velocity.
The linear velocity of a point on a rotating object is related to its angular velocity by the equation:
v = ω * r
where:
v is the linear velocity,
ω is the angular velocity, and
r is the radius or distance from the axis of rotation.
For the rear wheels:
Given that the dragster is speeding down the track at 150 m/s and the rear wheels have a diameter of 2 meters, we can calculate the radius (r) of the rear wheels:
r = diameter / 2 = 2 m / 2 = 1 m
The linear velocity of the rear wheels (v) is given as 150 m/s.
Using the equation v = ω * r, we can rearrange it to solve for ω:
ω = v / r
Substituting the values, we get:
ω = 150 m/s / 1 m = 150 rad/s
Therefore, the angular velocity of the rear wheels is 150 rad/s.
For the front wheels:
Given that the front wheels have a diameter of 40 cm, we need to calculate the radius (r) of the front wheels:
r = diameter / 2 = 40 cm / 2 = 20 cm = 0.2 m
Using the same equation v = ω * r, and substituting v = 150 m/s and r = 0.2 m, we can solve for ω:
ω = v / r
ω = 150 m/s / 0.2 m = 750 rad/s
Therefore, the angular velocity of the front wheels is 750 rad/s.
To calculate the angular velocities of the front and rear wheels, we can use the formula:
Angular velocity (ω) = Linear velocity (v) / Radius (r)
First, let's find the linear velocity of the dragster. It is given that the dragster is speeding at 150 m/s.
For the rear wheels:
1. The rear wheels have a diameter of 2m, so the radius (r) can be calculated as half of the diameter, which is 1m.
2. Using the formula, we can calculate the angular velocity:
Angular velocity (rear wheels) = Linear velocity (150 m/s) / Radius (1 m)
For the front wheels:
1. The front wheels have a diameter of 40 cm, so the radius (r) can be calculated as half of the diameter, which is 20 cm or 0.2 m.
2. Using the formula, we can calculate the angular velocity:
Angular velocity (front wheels) = Linear velocity (150 m/s) / Radius (0.2 m)
Therefore, the angular velocities of the front and rear wheels respectively are:
- Angular velocity (rear wheels) = 150 m/s / 1 m = 150 rad/s
- Angular velocity (front wheels) = 150 m/s / 0.2 m = 750 rad/s
150m/sec=2PI*radius/time
time for one rev = 2PI*radius/150
then w=2pi/timeabove=2PI*150/(2PI*radius)
= 150/radiusInMeters
check my thinking.