The axle of the toy top shown in the figure has a radius of 0.0100m and is so li

Question

The axle of the toy top shown in the figure has a radius of 0.0100m and is so light that its moment of interia is negligible compared to that of the disk. The disk is of uniform density and has a total mass of 0.200 kg and a radius of 0.0800 mm. A few turns of string are initially wrapped around the top's axle. The top is started by pulling on the string so as to create a constant tension.

A. What string tension is necessary to give the top an angular acceleration of 4.00 s^-2

B. Assuming the angular acceleration of part A and that the top starts from rest, how many turns of string must be wound around the shaft to give the top a final angular velocity of 20.0 s^-1

C. How much work must be done in order to launch the top as described in part B

D. How long will the starting process take

The axle of the toy top shown in the figure has a radius of 0.0100m and is so light that its moment of interia is negligible compared to that of the disk. The disk is of uniform density and has a total mass of 0.200 kg and a radius of 0.0800 mm. A few turns of string are initially wrapped around the top's axle. The top is started by pulling on the string so as to create a constant tension. What string tension is necessary to give the top an angular acceleration of 4.00 s^-2 Assuming the angular acceleration of part A and that the top starts from rest, how many turns of string must be wound around the shaft to give the top a final angular velocity of 20.0 s^-1 How much work must be done in order to launch the top as described in part B How long will the starting process take

Explanation / Answer

I = m*r*r/2 = 0.2*0.08*0.08/2 = 6.4*10^-4 kgm2

A) T*r = I * alpha

T = 6.4*10^-4 * 4/0.08 = 0.032 N

B) wf = 20 sec^-1

angle rotated = (wf^2)/2*alpha = 20*20/(2*4) = 50 rad = 50/3.14 rotation = 15.9 rotation

So, turns = 16 rotation approx.

C) Final KE = I*w*w/2 (this is rotational KE) = 0.128 J

So, work done must be equal to this.

Work = 0.128 J

D) t = wf/alpha = 20/4 = 5 sec

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.