2. A wheel is rotating at constant angular velocity of 1000 revolutions per minu

Question

2. A wheel is rotating at constant angular velocity of 1000 revolutions per minute (rpm). Calculate the number of radians the wheel rotates in one minute.

-Assume that the radius of the wheel is 10 cm. Calculate the distance in meters that a point on the rim of the wheel travels around the circumference in one minute.

-Calculate the magnitude of the tangential velocity of a point on the rim of the wheel (in meters per second).

-Calculate the angular acceleration of a whee that starts from rest and reaches angular velocity of 300 rad/s in 4 seconds. Anser in rad/s^2.

- Assume that the radius of the wheel is 15 cm and calculate the tangential acceleration of a point on the rim of the wheel (in m/s^2).

Explanation / Answer

2.a) w = 1000 rpm = (1000 * 2 * pi)/60 rad/s = 104.72 radians/second

Radians it will rotate in one minute = (1000 * 2 * pi) = 6283.15 radians

b) 10 cm = 0.1 m

Hence distance traveled by the point = 1000 * 2 * pi * r = 6283.15 * 0.1 = 628.315 m

c) Velocity = wr = 0.1 * 104.72 = 10.472 m/s

d) Angular Acceleration = wf - wo/t = (300 - 0)/4 = 75 rad/s^2

e) Tangential Acceleration = w.r = 0.15 * 75 = 11.25 m/s^2

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