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3 years ago

A grinding wheel is a uniform cylinder with a radius of 8.5cm and a mass of 0.580kg. Calculate

Physics

1 answer:

Kaylis [27]3 years ago

8 0

Answer:

(a) its moment of inertia about its center is 0.002095 kgm²

(b) Applied torque is 0.071813 Nm

Explanation:

Given;

Radius of the grinding wheel, R = 8.5cm

Mass of the grinding wheel, m = 0.580kg

Part (a) its moment of inertia about its center

I = ¹/₂MR²

I = ¹/₂(0.58)(0.085)²

I = 0.002095 kgm²

Part (b)

Given;

initial angular velocity, ωi = 1500rpm = 157.1 rad/s

final angular velocity, ωf = 1500rpm = 157.1 rad/s

Initial torque, τi = I x αi

αi = ωi / t

αi = 157.1 / 5 = 31.42 rad/s²

τi = 0.002095 x 31.42

τi = 0.06583 Nm

Final torque, τf = I x αf

αf = ωf / t

αf = 157.1 / 55 = 2.856 rad/s²

τf = 0.002095 x 2.856

τf = 0.005983 Nm

Applied torque = τi + τf

= 0.06583 Nm + 0.005983 Nm

= 0.071813 Nm

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