Classical Mechanics - Non Uniform Circular Motion

A particle constrained to move in a circle with 10-meter radius. At one instant, the particle’s speed is 10 meters per second and is increasing at a rate of 10 meters per second squared. The angle between the particle’s velocity and acceleration vector is

A. 0^o
B. 30^o
C. 45^o
D. 60^o
E. 90^o

(GR0177 #23)

Solution:



 = acceleration vector

The speed is increasing →   ∥ 

Given:
v = 10 m/s
r = 10 m
a_tan = 10 m/s²

a_c = v²/r = (10)²/(10) = 10 m/s²

tan θ = a_tan/a_c = 10/10 = 1 → θ = 45^o

Answer: C