Question

A disk is spinning initially at 60 rad/sec clockwise. if the disk begins to accelerate at 3 rad/sec counter-clockwise, how many rotations will it make before stopping

A) 10 rotations
B) 15 rotations
C) 20 rotations
D) 25 rotations

Answer 1

The disk will not make any rotations before stopping.

Step-by-step explanation:

To solve this problem, we need to first calculate the angular deceleration of the disk. The initial angular velocity is 60 rad/sec clockwise, and the acceleration is -3 rad/sec counter-clockwise. We can use the equation for angular acceleration, which is:

angular acceleration = (final angular velocity - initial angular velocity) / time

Plugging in the values, we get:

-3 rad/sec = (final angular velocity - 60 rad/sec) / time

Solving for time, we find that:

time = (final angular velocity - 60 rad/sec) / -3 rad/sec

Given that the disk will stop when the final angular velocity is 0 rad/sec, we can solve for the time it takes for the disk to stop. Plugging in 0 rad/sec as the final angular velocity, we get:

time = (0 rad/sec - 60 rad/sec) / -3 rad/sec

Simplifying the equation, we find that:

time = 20 seconds

Since each rotation is equal to 2π radians, we can calculate the number of rotations by dividing the total angle rotated by 2π. At any given time, the total angle rotated is given by the product of the initial angular velocity and time, plus half the product of the angular acceleration and the square of time. Plugging in the values, we get:

angle rotated = (60 rad/sec * 20 sec) + (0.5 * -3 rad/sec * (20 sec)^2)

Simplifying the equation, we find that:

angle rotated = 600π - 600π = 0 radians

Since the angle rotated is 0 radians, the disk will not make any rotations before stopping.