Question

Suppose you exert a force of 192 N tangential to a 0.295 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 19.6 N exerted 2.75 cm from the axis? (Enter the magnitude.)

rad/s²

Answer 1

(a)

F = tangential force applied = 192 N

R = radius of the grindstone = 0.295 m

m = mass of grindstone = 75 kg

Torque exerted is given as

= R F

= (0.295) (192)

= 56.64 Nm

b)

Moment of inertia of the grindstone is given as

I = (0.5) m R²

I = (0.5) (75) (0.295)²

I = 3.26 kgm²

= angular acceleration = ?

Torque is also given as

= I

56.64 = (3.26)

= 17.37 rad/s²

c)

f = frictional force = 19.6 N

r = distance from the axis = 2.75 cm = 0.0275 m

Torque equation can be given as

F R - f r = I

(192) (0.295) - (19.6) (0.0275) = (3.26)

= 17.21 rad/s²