A large uniform wheel that has radius R = 0.400 m is mounted on a frictionless a

Question

A large uniform wheel that has radius R = 0.400 m is mounted on a frictionless axle that passes through the center of the wheel. A light rope is wrapped around the wheel and a block of mass 3.00 kg is suspended from the free end of the rope. The system released from and the block moves downward as the wheel rotates clockwise. As the block descends the tension in the rope is 15.0 N. a) What is the acceleration of the block? b) What is the angular speed of the wheel when the block is 1.20 m below its initial position?

Explanation / Answer

part a )

mg -T = ma

a = g - T/m

a = 9.8 - 15/3

a = 4.8 m/s^2

part b )

vy^2 = uy^2 + 2a*s

uy = 0

a = 4.8 m/s^2

s = 1.2 m

v = sqrt(2*4.8 * 1.2 )

v = 3.394 m/s

we know

w = v/r = 3.394/0.400 = 8.485 rad/s

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