1 A wheel spins through 27 revolutions per minute Find the a

1.

A wheel spins through 27 revolutions per minute. Find the angular velocity and the linear velocity if the radius of the wheel is 1.7 feet.

v=

w=

2.A bicycle with 18-in.-diameter wheels has its gears set so that the chain has a 7-in. radius on the front sprocket and 3-in. radius on the rear sprocket. The cyclist pedals at 200 rpm.

a.Find the linear speed of the bicycle in in/min=

b.How fast is the bike moving in mph?

Solution

1.

A wheel spins through 27 revolutions per min,radius of the wheel is 1.7 feet

angular velocity =revolutions per minute*(2 rad/rev)

angular velocity =(27rev/min)*(2 rad/rev)

angular velocity =169.646 rad/min

linear velocity v = radius *angular velocity

linear velocity v = 1.7 *169.646

linear velocity v = 288.4 ft/min