Problem 22.79 A current of 1.8 A flows through a circular coil of wire with 56 t

Question

Problem 22.79 A current of 1.8 A flows through a circular coil of wire with 56 turns and a radius of 0.74 cm. The coil rotates in a uniform 0.12-T magnetic field.

Part A

What is the maximum torque exerted on the loop of wire? Express your answer to two significant figures.

=_________________N*m

Part B

The time-averaged torque on the loop is half its maximum value. If the moment of inertia of the loop is 2.0×105kgm2 and the loop undergoes constant angular acceleration, in what time will it have reached its maximum angular speed of 2700 rev/min ?

Express your answer to two significant figures and include appropriate units.

Explanation / Answer

A.

Max torques is given by:

tau = N*i*A*B*sin theta

tau)max = N*i*A*B

tau)max = 56*1.8*pi*0.0074^2*0.12 = 2.08*10^-3 N-m

B.

tau = tau)max/2 = 1.04*10^-3 N-m

Now we know that:

tau = I*alpha

alpha = angular acceleration

I = moment of inertia

alpha = tau/I

alpha = 1.04*10^-3/(2*10^-5) = 52 rad/sec^2

Now using the equation

wf = wi + alpha*t

wi = 0 rad/sec

wf = 2700 rev/min = 282.74 rad/sec

t = (wf - wi)/alpha

t = 282.74/52 = 5.44 sec

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