Question

A wheel with a 30-cm radius is rotating at a rate of 3 radians/sec. What is the linear speed of a point on its rim, in meters per minute?

Transformations of functions
ANSWERED
asked 2021-06-14
A wheel with a 30-cm radius is rotating at a rate of 3 radians/sec. What is the linear speed of a point on its rim, in meters per minute?

Answers (1)

2021-06-15

Use the formula relating the linear speed vv and angular speed ωω: v=ωr
where rr is the radius.
Substitute \(\omega=3 \text{ radians}/sec\) and r=30 cm:
v=(3 rad/s)(30 cm)
v=90 cm/s
Convert to m/min: \(\displaystyle{v}={90}{c}\frac{{m}}{{s}}\cdot{1}\frac{{m}}{{100}}{c}{m}\cdot{60}\frac{{s}}{{1}}\min={54}\frac{{m}}{\min}\)

0
 
Best answer

expert advice

Have a similar question?
We can deal with it in 3 hours

Relevant Questions

asked 2021-05-08
A high-speed sander has a disk 4.00 cm in radius that rotates about its axis at aconstant rate of 1265 rev/min.Determine
(a) the angular speed of the disk in radians persecond,
rad/s
(b) the linear speed of a point 2.2 cmfrom the disk's center,
m/s
(c) the centripetal acceleration of a point on the rim, and
\(\displaystyle\frac{{m}}{{s}^{{{2}}}}\)
(d) the total distance traveled by a point on the rim in1.96 s.
m
asked 2021-02-19
A 10 kg objectexperiences a horizontal force which causes it to accelerate at 5 \(\displaystyle\frac{{m}}{{s}^{{2}}}\), moving it a distance of 20 m, horizontally.How much work is done by the force?
A ball is connected to a rope and swung around in uniform circular motion.The tension in the rope is measured at 10 N and the radius of thecircle is 1 m. How much work is done in one revolution around the circle?
A 10 kg weight issuspended in the air by a strong cable. How much work is done, perunit time, in suspending the weight?
A 5 kg block is moved up a 30 degree incline by a force of 50 N, parallel to the incline. The coefficient of kinetic friction between the block and the incline is .25. How much work is done by the 50 N force in moving the block a distance of 10 meters? What is the total workdone on the block over the same distance?
What is the kinetic energy of a 2 kg ball that travels a distance of 50 metersin 5 seconds?
A ball is thrown vertically with a velocity of 25 m/s. How high does it go? What is its velocity when it reaches a height of 25 m?
A ball with enough speed can complete a vertical loop. With what speed must the ballenter the loop to complete a 2 m loop? (Keep in mind that the velocity of the ball is not constant throughout the loop).
asked 2021-04-03
A wheel is rotating freely at angular speed 800 rev/min on ashaft whose rotational inertia is negligible. A secod wheel,initially rest and with twice the rotational inertia of the first,is suddenly coupled to the same shaft.
A) what is the angular speedof the resultant combination of the shaft and the two wheels?
B)What fraction of the orginial rotational kinetic energy is lost?
asked 2021-06-10
Water flows through a water hose at a rate of \(Q_{1}=680cm^{3}/s\), the diameter of the hose is \(d_{1}=2.2cm\). A nozzle is attached to the water hose. The water leaves the nozzle at a velocity of \(v_{2}=9.2m/s\).
a) Enter an expression for the cross-sectional area of the hose, \(A_{1}\), in terms of its diameter, \(d_{1}\)
b) Calculate the numerical value of \(A_{1},\) in square centimeters.
c) Enter an expression for the speed of the water in the hose, \(v_{1}\), in terms of the volume floe rate \(Q_{1}\) and cross-sectional area \(A_{1}\)
d) Calculate the speed of the water in the hose, \(v_{1}\) in meters per second.
e) Enter an expression for the cross-sectional area of the nozzle, \(A_{2}\), in terms of \(v_{1},v_{2}\) and \(A_{1}\)
f) Calculate the cross-sectional area of the nozzle, \(A_{2}\) in square centimeters.
...