Adog sits 2.6 m from the center of a merry- go-round. a) if the dog undergoes a 1.7 m/s^2 centripetal acceleration, what is the dog's linear speed? answer in units of m/s. b) what is the angular speed of the merry-go- round? answer in units of rad/s.

a) v= 2.1 m/s

b) ω = 0.807 rad/s

Explanation

Conceptual analysis :

The dog and the merry-go- round describes a circular motion, then, the following formulas apply :

Formula (1)

v = ω *r   Formula (2)

Where:

: Centripetal acceleration(m/s²)

v: linear speed or tangential (m/s)

r :  radius of the circle (m)

ω : angular speed ( rad/s)

Data

r= 2.6 m

=  1.7 m/s²

Problem develpment

a) We replace data in the formula 1 to calculate the dog's linear speed(v):

v= 2.1 m/s

b)We replace data in the formula 2 to calculate the angular speed of the merry-go- round (ω).

v = ω *r

2.1 = ω *2.6

ω = 2.1/2.6

ω = 0.807 rad/s

b. a lightning bug, plug of grass, and a worm