Question

A cylinder of radius R = 6.0 cm is on a rough horizontal surface. The coefficient of kinetic friction between the cylinder and the surface is 0.30 and the rotational inertia for rotation about the axis is given by MR2/2, where M is its mass. Initially it is not rotating but its center of mass has a speed of 7.0m/s. After 2.0 s the speed of its center of mass and its angular

velocity about its center of mass, respectively, are:
A. 1.1m/s, 0
B. 1.1m/s, 19 rad/s
C. 1.1m/s, 98 rad/s
D. 1.1m/s, 200 rad/s
E. 5.9m/s, 98 rad/s

Answer 1

To determine the speed of the center of mass and the angular velocity of the cylinder after 2.0 seconds, we need to consider the rotational motion and the kinetic energy of the system.

Step-by-step explanation:

To determine the speed of the center of mass and the angular velocity of the cylinder after 2.0 seconds, we need to consider the rotational motion and the kinetic energy of the system.

First, we calculate the final speed of the center of mass by using the equation:

Vf = Vi + (acceleration * time)

Where Vi is the initial speed of the center of mass, acceleration is the rate of change of speed, and time is the duration.

Then, we calculate the final angular velocity using the equation:

ωf = ωi + (angular acceleration * time)

Where ωi is the initial angular velocity, angular acceleration is the rate of change of the angular velocity, and time is the duration. Plugging in the given values, we can calculate the final speed and angular velocity to be 1.1 m/s and 98 rad/s, respectively. Therefore, the correct option is C. 1.1m/s, 98 rad/s.