Question

A disk with an initial angular velocity ω₀ = 5.5 rad/s experiences a constant angular acceleration of α = 2.5 rad/s² for a time period t = 95 s. Please answer the following questions.

a) Determine the final angular velocity of the disk.
b) Find the angular displacement of the disk during this time.
c) Calculate the torque acting on the disk.
d) All of the above

Answer 1

The angular displacement of a disk with an initial angular velocity of 5.5 rad/s, constant angular acceleration of 2.5 rad/s², over a time period of 95 seconds is calculated using the kinematic equation for rotational motion. Substituting the given values into the equation, the displacement can be found.

Step-by-step explanation:

The student's question asks about calculating the angular displacement of a disk given its initial angular velocity, constant angular acceleration, and the time interval during which it is accelerating. To find the angular displacement θ (theta) during the time interval, one can use the kinematic equation for rotational motion:

θ = ω0t + ½αt2

Where:

• ω0 is the initial angular velocity (5.5 rad/s in this case)
• α is the angular acceleration (2.5 rad/s²)
• t is the time period (95 s)

Applying these values, we find the angular displacement of the disk:

θ = (5.5 rad/s × 95 s) + ½(2.5 rad/s² × 95 s2)

This equation gives us the total radians through which the disk has rotated in the given time period under constant angular acceleration.