3. 20pts A sphere with a mass of 5 kg and a radius of 25 cm is (the axis of rota

Question

3. 20pts A sphere with a mass of 5 kg and a radius of 25 cm is (the axis of rotation is the z-axis). The direction rotat sphere. of rotation around its center in the x-y plane What is its angular the is counter-clockwise when viewed from above the speed in radians per second (rad/s)? If a force of 7.5 N is applied to the edge of the sphere in the direction, what will be the resulting angular acceleration of the sphere? Be sure to include the sign of this angular acceleration. What will be the angular speed after the force has been applied for 3.0 seconds? How long does the 7.5 N force have to be applied in order to bring the sphere to astop?

Explanation / Answer

A) angular sped is w = 600 rpm = 600*2*3.142/60 = 62.84 rad/s

B) Torque T = I*alpha

I is moment of inertia of solid sphere = (2/5)*m*r^2=(2/5)*5*0.25^2 = 0.125

T = F*r*sin(90) = 7.5*0.25 = 1.875 N-m

alpha = T/I = 1.875/0.125 = 15 rad/s^2

sign is negative for clockwise rotation alpha = 15 rad/s^2

C) wf = (wi)+(alpha*t) = 62.84+(15*3) = 107.84 rad/s
D) wf = 0 rad/s

wi = 62.84 rad/s

alpha = 15

then t = (wi)/alpha = 62.84/15 = 4.18 S

Related Questions

Navigate

• Browse (All)
• Browse 3
• Subjects

---

---

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