A pulley of radius 10cm turns at 6 revolutions per second. What is the linear velocity of the belt driving the pulley in meters per second? 1.67 m/s
3.77 m/s
376.99 m/s
166.67 m/s

v = 3.77 m/s

Step-by-step explanation:

Uniform Circular Motion

It's a movement in which an object moves along the circumference of a circle. It can also be defined as a rotation along a circular path.

The angular speed can be calculated in two different ways:

Where:

v = tangential or linear speed

r = radius of the circle described by the rotating object

Also:

Where:

f = frequency

The frequency is calculated when the number of revolutions n and the time t are known:

The pulley turns at n=6 revolutions per t= 1 second, thus:

f = 6 Hz

The angular speed is:

The linear speed can be calculated by solving the first equation for v:

The radius is converted to meters: r=10 cm = 0.1 m. Calculate the speed:

v = 3.77 m/s

b.) 160 miles on a 5 gallons car

step-by-step explanation:

240/10=24 miles/gallon

160/5=32 miles/gallon

30/1=30 miles/gallon

168/6= 28 miles/gallon

32 miles/gallon is the most amount, so this is the best.

y/x of point b= y/x of point a

step-by-step explanation:

(i got the same question, this was the correct answer.)