Question 1: (Rotational Motion) A uniform solid sphere of radius R = 0.200 m and

Question

Question 1: (Rotational Motion)

A uniform solid sphere of radius R = 0.200 m and mass M = 1.80 kg starts from the bottom of an inclined plane and rolls up the incline without slipping. The initial translational speed of the center of mass of the sphere is vi = 8.40 m/s.

(a) What is the initial angular velocity wi of the sphere at the bottom?

(b) What is the total kinetic energy at the bottom?

(c) What is the height vertical H the sphere reaches when it momontarily comes to rest?

Question 2: (Torque and angular acceleration)

A solid, uniform cylinder of mass M = 3600 kg and radius R = 4.0 m can rotate about an axis at the center. The cylinder is subjected to the two steady forces applied at the opposite ends of a diameter shown. As you can see, the forces are tangent to the cylinder rim.
(a) Compute the moment of inertia I about the center.
(b) What is the magnitude | |of the net torque about the center?
(c) What is the cylinders angular acceleration ?
(d) Assume the cylinder starts it rotation from rest when subjected to the two steady forces shown. What is the cylinders angular velocity after a time period of 60.0 seconds?

A uniform solid sphere of radius R = 0.200 m and mass M = 1.80 kg starts from the bottom of an inclined plane and rolls up the incline without slipping. The initial translational speed of the center of mass of the sphere is vi = 8.40 m/s. What is the initial angular velocity wi of the sphere at the bottom? What is the total kinetic energy at the bottom? What is the height vertical H the sphere reaches when it momontarily comes to rest? Question 2: (Torque and angular acceleration) A solid, uniform cylinder of mass M = 3600 kg and radius R = 4.0 m can rotate about an axis at the center. The cylinder is subjected to the two steady forces applied at the opposite ends of a diameter shown. As you can see, the forces are tangent to the cylinder rim. Compute the moment of inertia I about the center. What is the magnitude | Ï |of the net torque about the center? What is the cylinderâs angular acceleration I^+- ?Assume the cylinder starts it rotation from rest when subjected to the two steady forces shown. What is the cylinderâs angular velocity Ï after a time period of 60.0 seconds?

Explanation / Answer

1. a) Angular velocity, about COM = 0 and about point of contact = vr = 1.68 rad/s

{Note: angular velo and parameters like those are rotational parameters and you must mention the axis of rotation considered while defining those or asking for those things, which you lacked in the question}

b) KE = m*v*v/2 = 63.504 J

c) KE at top = 0. PE = mgH = 1.8*9.8*H = 63.504 >>> H = 3.6 m

2. a) MOI = m*r*r/2 = 28800 kg.m2

b) Since, both the torque are additive, anticlockwise rotation.

T = 2*F*r = 200 Nm

c) alpha = T/I = 6.94*10^-3 raad/s2

d) w = alpha * t = 0.4167 raad/sec

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