5. (a)A metal ball of mass 388 g at the end of a 1.03 m long wire rotates with a

Question

5.

(a)A metal ball of mass 388 g at the end of a 1.03 m long wire rotates with an angular speed of 90 rev/min (90 2 rad/min). What is the rotational kinetic energy of the ball?

(b)The angular velocity of a wheel that can rotate in the xy-plane around a fixed axle oriented along the z-axis varies with time as = (w1t - w2t2)k, where w1 and w2 are constants. Assuming that the wheel starts at t = 0 with a mark on its edge sitting on the positive x-axis, where is the mark the next time the wheel comes to rest? (Use any variable or symbol stated above as necessary.)

can someone sove question no. 5

Explanation / Answer

(a) KE = (0.5) ( I ) (W)^2

I = the inertia of the object, a rod is (1/12) ( M ) ( R^2 )
W = (rpm*2*pi)/60

so, w = (90* 2 * pi)/60 = 9.42 rad/sec
so, I = (1/12) * 0.388 * 1.032 = 0.0343 kg.m2

K.E. =0.5 * 0.0343 * 9.42^2 = 1.522 joule.......Ans.

(b) omega = [(w1)*t - (w2)*(t2)]k = (w1)kt - (w2)kt^2
Rotational Distance = (1/2)(w1)kt^2 - (1/3)(w2)kt^3

omega = 0 when t=0 also (w1) = (w2)t this means t = (w1)/(w2)

Rotational Distance = (1/2)(w1)k[(w1)/(w2)]^2 - (1/3)(w2)k[(w1)/(w2)]^3
= k{[(w1)/(w2)]^2[(1/2)(w1) - (1/3)(w2)(w1)/(w2)]}
= k{[(w1)/(w2)]^2[(1/2)(w1) - (1/3)(w1)]
= k{[(w1)/(w2)]^2[(3-2)/6](w1)
= (1/6)(w1)k{[(w1)/(w2)]^2

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