Answer the following questions related to the concept of angular velocity.
PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Torque and Rotational Dynamics · Torque and Rotational Dynamics
Problem
Answer the following questions related to the concept of angular velocity.
(i) Define average angular velocity and instantaneous angular velocity.
(ii) Explain, using the idea of a vanishingly small time interval, how the expression for instantaneous angular velocity is obtained from the definition of average angular velocity.
(iii) A wheel has its angular displacement varying with time according to θ=5t−2t2, where θ is in radians and t in seconds. Calculate the average angular velocity of the wheel between t=0s and t=2s.
(iv) Determine the instantaneous angular velocity at t=1s for the same wheel and compare its magnitude with the average value obtained in part (iii).