Question

For College Physics. Please type response as it is sometimes difficult to read when a picture is uploaded. Thank you!

Answer the following:

Describe angular velocity and angular acceleration. In your own words, explain the relationship between linear and angular quantities. In your own words, explain rotational kinetic energy and moment of Inertia.

Answer 1

Rate of change of angular displacement of a body is knows called angular velocity. It the angle turned by a body per unit time. It's SI unit is radian per seconds. Angular acceleration is the rate of change of angular velocity. It's SI unit is radian per second square. It is basically the measurement of how the angular velocity of a body is changing.

For a given angular quantity, the linear quantities are directly proportional to the distance of the body or particle from the center. It's also proportional to the Sine of angle between the distance vector and angular quantity vector. For example, liner velocity = r (distance from centre) * w (angular velocity) * Sin(theta) (the angle between the r and w vector)

Rotational kinetic energy is the energy possessed by a particle or a body executions rotational motion about any axis. A particle or body can have either or both translation kinetic energy or rotational kinetic energy. The pure rolling of a ball down an inclined plane is an example of a body having both forms of kinetic energy. A fan moving about a fixed axis is an example of a body just having rotational kinetic energy.

Moment of inertia is the body's tendency to resist angular acceleration. It's the sum of the sum of the products of the mass of each particle in the body with the square of its distance from the axis of rotation.