. Advertisement .

..3..

. Advertisement .

..4..

......... ADVERTISEMENT .........

..8..

**Learning goal:**

*I*

_{t}rotating at a constant angular velocity

*ω*

_{i}around an axis through the center and perpendicular to the plane of the disk (the disk’s “primary axis of symmetry”). The axis of the disk is vertical and the disk is supported by frictionless bearings. The motor of the turntable is off, so there is no external torque being applied to the axis. Another disk (a record) is dropped onto the first such that it lands coaxially (the axes coincide). The moment of inertia of the record is

*I*

_{r}. The initial angular velocity of the second disk is zero. There is friction between the two disks. After this “rotational collision,” the disks will eventually rotate with the same angular velocity.

......... ADVERTISEMENT .........

..8..

**Part A**

*ω*

_{f}, of the two disks?

*Express ω*

_{f }in terms of I_{t}, I_{r}and ω_{i}.*ω*

_{f }=

**Part B**

*K*

_{f}, of the two spinning disks?

*Express the final kinetic energy in terms of I*

_{t}, I_{r}and the initial kinetic energy K_{i}of the two-disk system. No angular velocities should appera in your answer.*K*

_{f}=

**Part C**

*Δ*t before reaching the final angular velocity (

*Δ*t is the time interval between the moment when the top disk is dropped and the time that the disks begin to spin at the same angular velocity). What was the average torque, (

*τ*), acting on the bottom disk due to friction with the record?

*Express the torque in terms of I*

_{t}, w_{i}, w_{f}and Δt.*τ*) =

An angular velocity is the amount of speed that an object experiences when turning around a certain location. The measurement is in radsec. It is also referred to as the rotational velocity. It refers to the degree of changes in angular displacement regard to time. It is a quantity vector that is measurable and direction.

## 1 Answer