A dragster is speeding down the track at 150 m/s. Its rear wheels are 2 m in diameter, and its front
wheels are 40 cm in diameter. What are the angular velocities of the front and rear wheels, respectively?
At what angle is a force directed if its horizontal component is 10 N and the vertical component is 15 N?
omega r = v
r in meters
v in meters/sec
omega in radians/sec
rear
omega * 1 = 150
front
omega * 0.20 = 150
tan theta = y component / x component = 1.5
tan^-1 (1.5)
56.3 degrees above horizontal
To find the angular velocities of the front and rear wheels, we need to relate the linear velocity of the dragster to the angular velocity of the wheels.
First, we need to convert the diameter of the wheels to their radii:
Rear wheels: diameter = 2 m, so radius = 1 m
Front wheels: diameter = 40 cm = 0.4 m, so radius = 0.2 m
The linear velocity of a point on the edge of a wheel is given by the equation:
v = ω * r
where v is the linear velocity, ω (omega) is the angular velocity, and r is the radius of the wheel.
For the rear wheels:
v = 150 m/s (given)
r = 1 m (rear wheel radius)
ω (rear) = v / r
Substituting the values:
ω (rear) = 150 m/s / 1 m = 150 rad/s
For the front wheels:
v = 150 m/s (given)
r = 0.2 m (front wheel radius)
ω (front) = v / r
Substituting the values:
ω (front) = 150 m/s / 0.2 m = 750 rad/s
Therefore, the angular velocity of the rear wheels is 150 rad/s, and the angular velocity of the front wheels is 750 rad/s.