Answer:
(a)a= 2.222 m/s²
(b)angle= 26.973 rad
(c) 4.295 revolutions
Explanation:
Given data
Radius=0.3 m
Linear velocity =0 m/s to 6 m/s
time taken=2.7 s
To find
(a) Angular acceleration in rad/s²
(b) Angle in radian
(c) Revolutions
Solution
For Part (a) of question
a) Use the equation acceleration = Alpha/R.........eq(i)
First find the linear acceleration
a = (v₂ – v₁)/(t₂ – t₁)
a= (6-0)/(2.7-0)
a= 2.222 m/s²
Put the value into the equation and solve for alpha:
angular acceleration=2.22/0.3
angular acceleration= 7.4 rad/s^2
For Part (b) of question
B) Use the equation өf = ө₀ + w₀t + (1/2)alpha×t²
This reduces to өf = (1/2)alpha×t²
Put the values into the equation
angle=(1/2)(7.4)(2.7)²
angle= 26.973 rad
For Part (c) of question
C) Convert the previous answer into revolutions
26.973 rad * (1rev/2π rad)
= 4.295 revolutions
