2. A roller 0.4 m diameter rolls down a slope starting from rest. It takes 20 seconds make 8 complete rotations along the sloping surface accelerating uniformly as it moves.
Calculate the following:
i. The angular velocity at the end.
ii. The linear velocity at the end.
iii.The angular acceleration.
iv. The linear acceleration.
Circumference = pi*d = 3.14 * 0.4 = 1.26 m.
1. Va = 8rev/20s * 6.28rad/rev = 2.51 rad/s.
2. V = 8rev/20s * 1.26m/rev = 0.502 m/s.
3. Va = Vo + a*t.
2.51 = 0 + a*20,
a = 0.126 rad/s^2.
4. V = Vo + a*t.
0.502 = 0 + a*20,
a = 0.025 /s^2.