During 0.19 s, a wheel rotates through an angle of 2.42 rad as a point on the periphery of the wheel moves with a constant speed of 2.88 m/s. What is the radius of the wheel?
A highway curve with a radius of 800 m is banked properly for a car traveling 100 km/h. If a 1620- kg Porshe 928S rounds the curve at 220 km/h, how much sideways force must the tires exert against the road if the car does not skid?
v=rw w=2.42/0.19=12.74rad/s r=2.88/12.74=0.226m 2)Banking angle=v^2/rg=27.7^2/800g=61.1^2/rg r=(61.1/27.7)^2*800=3892m F=1620(61.1)(61.1)/3892=1554N
During 0.19 s, a wheel rotates through an angle of 2.42 rad as a point on the periphery of the wheel moves with a constant speed of 2.88 m/s. What is the radius of the wheel?
w=2.42rad/.19 sec= you do it.
speed=2.88m/s=wr=2.42/.19 * r
r= 2.88/(2.42/.19)
To find the radius of the wheel, we can use the formula for angular velocity:
ω = Δθ / Δt
where ω is the angular velocity, Δθ is the change in angle, and Δt is the change in time.
In this case, we are given that the wheel rotates through an angle of 2.42 rad in a time of 0.19 s. So, we can plug these values into the formula:
ω = 2.42 rad / 0.19 s
Simplifying this, we find:
ω = 12.73 rad/s
Next, we can use the formula for linear velocity:
v = rω
where v is the linear velocity, r is the radius of the wheel, and ω is the angular velocity.
We are given that the point on the periphery of the wheel moves with a constant speed of 2.88 m/s. So, we can plug in the values:
2.88 m/s = r * 12.73 rad/s
Now we can solve for r:
r = 2.88 m/s / 12.73 rad/s
Calculating this, we find:
r ≈ 0.226 m
Therefore, the radius of the wheel is approximately 0.226 meters.