A 250 g 21-cm-diameter plastic disk is spun on an axe through its center by an e

Question

A 250 g 21-cm-diameter plastic disk is spun on an axe through its center by an electric motor. What torque must the motor supply to take the disk from 0 to 1900 rpm in 5.0 s? Express your answer using two significant figures The photograph below shows a girl pushing on a large stone sphere. The sphere has a mass of 8200 kg and a radius of 90 cm and floats with nearly zero friction on a thin layer of pressurized water Support. That she pushes on the sphere tangent to its surface with a steady force of F = 25 n and that the pressured water provides a frictionless support. How long will it take her rotate the sphere one time, starting from rest? Express your answer to two significant figures and include the appropriate units

Explanation / Answer

part a:

we know that torque=moment of inertia*angular acceleration

here initial angular speed=0 rad/s

final angular speed=1900 rpm=198.8675 rad/s

then angular acceleration=(final angular speed-initial angular speed)/time

=39.7935 rad/s^2

moment of inertia of a disk=0.5*mass*radius^2

=0.5*0.25*(0.21/2)^2=1.378125*10^(-3) kg.m^2

then torque needed=moment of inertia*angular acceleration

=0.0548 N.m

problem 7.50:

torque applied=force*radius=25*0.9=22.5 N.m

moment of inertia=(2/5)*mass*radius^2

=(2/5)*8200*0.9^2=2656.8 kg.m^2

then angular acceleration=torque/moment of inertia

=8.4688*10^(-3) rad/s^2

let time taken for one rotation is t seconds

angle completed=2*pi rad

using the formula:

angle travelled=initial angular speed*time+0.5*angular acceleration*time^2

==>2*pi=0*t+0.5*8.4688*10^(-3)*t^2

==>t=38.52 seconds

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