Rotations An electric motor rotating a workshop-grinding wheel of radius 0.5 m a

Question

Rotations An electric motor rotating a workshop-grinding wheel of radius 0.5 m at a rate of 1000 rad/switched off. Assume constant negative angular acceleration of magnitude 2.00 rad/s^2. What is the initial linear velocity of a point on the rim of the wheel? What is the linear tangential acceleration of the wheel? How long does it take for the grinding wheel to stop? Through how many radians has the wheel turned before stopping? What is the total distance traveled by a point on the rim of the wheel before coming to rest

Explanation / Answer

here,

radius , r = 0.5 m

initial angular speed , w0 = 1000 rad/s

angular accelration , alpha = - 2 rad/s^2

a)

the initial linear velocity , v0 = r * w0

v0 = 0.5 * 1000 = 500 m/s

b)

the linear tangential accelration , a = alpha * r

a = - 2 * 0.5 m/s^2

a = - 1 m/s^2

c)

let time taken to stop be t

0 = v0 + a * t

0 = 500 - 1 * t

t = 500 s

d)

let the angle covered be theta

w^2 - w0^2 = 2 * alpha * theta

0 - 1000^2 = 2 * (-2) * theta

theta = 2.5 * 10^5 rad

e)

the distance travelled , s = r * theta

s = 1.25 * 10^5 m

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