Question

(a) What is the magnitude of the tangential acceleration of a bug on the rim of an 11.5-in.-diameter disk if the disk accelerates uniformly from rest to an angular speed of 77.0 rev/min in 3.50 s?

(b) When the disk is at its final speed, what is the magnitude of the tangential velocity of the bug?

(c) One second after the bug starts from rest, what is the magnitude of its tangential acceleration?

(d) One second after the bug starts from rest, what is the magnitude of its centripetal acceleration?

(e) One second after the bug starts from rest, what is its total acceleration? (Take the positive direction to be in the direction of motion.)

Answer 1

(a) What is the tangential acceleration of a bug on the rim of a 11.5.0-in.-diameter disk if the disk accelerates uniformly from rest to an angular speed of 77.0 rev/min in 3.50 s?

w = 2πf = 2 * 3.1416 * 77/60 = 8.042 rad/s

R = 11.5 * 0.0254/2 = 0.1460 m

α = Δw/Δt = 8.042/3.50 = 2.2977 rad/s2

a = R α = 0.1460* 1.7453 = 0.33546 m/s²

(b) When the disk is at its final speed, what is the tangential velocity of the bug?

v = R w = 0.1460 * 8.042 = 1.17 m/s

(c) One second after the bug starts from rest, what is its tangential acceleration?

α = Δw/Δt = 8.042/3.50 = 2.2977 rad/s2

a = R α = 0.1460 * 2.2977 = 0.33546 m/s²

(d) One second after the bug starts from rest, what is its centripetal acceleration?

w = α t = 2.2977 rad/s

a = R w^2 = 0.1460 * 2.2977 *2.2977 = 0.77079 m/s2

(e) One second after the bug starts from rest, what is its total acceleration?

a = square root (0.33546*0.33546+0.77079*0.77079) = 0.840 m/s2

cos^-1 (0.7707 /0.840) = 23.45° from the radially inward direction

I hope help you......!!