Problem 6. A solid disk of radius 10.0cm and mass 3.00kg is rotating clockwise i

Question

Problem 6. A solid disk of radius 10.0cm and mass 3.00kg is rotating clockwise in the x-y plane about a vertical axis passing through its center. It is rotating at 90.0rpm. (a) What is the magnitude of its angular velocity in radians/sec? (b) What is the direction of its angular velocity? (c) What is the tangential speed of a point located 3.00 cm from the axis? (d) What is the magnitude of the radial acceleration of a point on the rim? A contant angular acceleration now brings the disk to rest in 4.70s. (e) What is the magnitude of the angular acceleration? (f) What is the direction of the angular acceleration? (g) How far does a point on the rim travel from the time the disk starts slowing down till it comes to rest?

Explanation / Answer

(a)

w = 90 rpm ( 2pi rad/ 60 s) = 9.42 rad/s

(b) from the right hand rule the direction is into the page

(c)

v= rw = 0.03 m * ( 9.42) = 0.2826 m/s

(d)

a_r = r w^2 = 0.1( 9.42)^2 = 8.87 m/s^2

(e)

Apply rotational kinematic equation

wf - wi = alpha t

0-9.42 = alpha ( 4.70)

alpha = -2 rad/s^2

(f) from the right hand rule the direction is into the page

(g) theta = wi t + 1/2 ( alpha) t^2

= 9.42 ( 4.7) + 1/2 ( -2) ( 4.7)^2

=22.18 rad

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

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