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23 September, 09:14

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

a. its moment of inertia about its center.

b. the applied torque needed to accelerate it from rest to 1500rpm in 5.00s if it is known to slow down from 1500rpm to rest in 55.0s.

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  1. 23 September, 09:17
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    (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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