Question

Suppose you exert a force of 212 N tangential to a 0.215 m radius 75.0 kg grindstone (a solid disk). (Give your answers to at least 2 decimal places.)

(a)

What torque (in N · m) is exerted? (Enter the magnitude.)

N · m

(b)

What is the angular acceleration (in rad/s²) assuming negligible opposing friction? (Enter the magnitude.)

rad/s²

(c)

What is the angular acceleration (in rad/s²) if there is an opposing frictional force of 20.6 N exerted 1.75 cm from the axis? (Enter the magnitude.)

rad/s²

Answer 1

given
F_tan = 212 N
R = 0.215 m
M = 75 kg

a) Torque exerted, T = F_tan*R*sin(theta)

= 212*0.215*sin(90)

= 45.6 N.m <<<<<<<-----------Answer

b) Moment of inertic of the grindtone,

I = 0.5*M*R^2

= 0.5*75*0.215^2

= 1.73 kg.m^2

angular acceleration, alfa = T/I

= 45.6/1.73

= 26.4 rad/s^2 <<<<<<<----------Answer

c) angular acceleration, alfa' = net torque/I

= (T_applied - T_friction)/I

= (45.6 - 20.6*0.0175*sin(90))/1.73

= 26.1 rad/s^2    <<<<<<<----------Answer