A uniform disk of mass M = 5.3 kg has a radius of 0.10 m and is pivoted so that

Question

A uniform disk of mass M = 5.3 kg has a radius of 0.10 m and is pivoted so that it rotates freely about its axis. A string wrapped around the disk is pulled with a force F equal to 21 N.

(a) What is the torque being exerted by this force about the rotation axis?
N ? m

(b) What is the angular acceleration of the disk?
rad/s2

(c) If the disk starts from rest, what is its angular speed after 5.6 s?
rad/s

(d) What is its kinetic energy after the 5.6 s?
J

(e) What is the angular displacement of the disk during the 5.6 s?
rad

(c) Find the maximum angle of the incline for which the ball will roll without slipping.

?max =

A uniform disk of mass M = 5.3 kg has a radius of 0.10 m and is pivoted so that it rotates freely about its axis. A string wrapped around the disk is pulled with a force F equal to 21 N. (a) What is the torque being exerted by this force about the rotation axis? (b) What is the angular acceleration of the disk? rad/s^2 (c) If the disk starts from rest, what is its angular speed after 5.6 s? rad/s (d) What is its kinetic energy after the 5.6 s? J (e) What is the angular displacement of the disk during the 5.6 s? rad (c) Find the maximum angle of the incline for which the ball will roll without slipping. ?max =

Explanation / Answer

Given data:

the mass of the disk, M = 5.3 kg

radius of the disk , R = 0.10 m

the force F = 21 N

(a)

T(torque) = F R = 21 * 0.10 = 2.1 N-m

the torque being exerted by this force about the rotation axis is 2.1 N-m.

(b)

the moment of inertia of the disk,

I = 1/2 M R2 = 1/2*5.3 *0.12 = 0.0265 kgm2

the angular acceleration,

? = T / I = 2.1 /0.0265 = 79.24 rad/ s2

the angular acceleration of the disk is 79.24 rad/s^2

(c) the angular speed of the disk after 5.6 s,

? = ? t = 79.24*5.6 = 443.744 rad/ s

(d)

the kinetic energy,

KE = 1/2 I ?2 = (0.0265/ 2)* 443.7442 = 2609.04 J

(e)

the angular displacement,

? = 1/2 ? t2 = (79.24 / 2) * 5.6^2 = 1242.48 rad

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