A wheel with a radius of 0.75 m starts from rest and accelerates clockwise. The

Question

A wheel with a radius of 0.75 m starts from rest and accelerates clockwise. The angular acceleration of the wheel is given by alpha = 6t - 4(rad/s^2). a. what is angular velocity at t = 4 seconds? b. How long will it take to rotate 3 revolutions? If you spin pizza dough from rest with an angular acceleration of 5 rad/s^2. a. How many radians will the pizza spin through in 10 seconds? b. What is the angular velocity of the pizza after 5 seconds? A carousel ride starts from rest and increases speed at a constant rate until the rider 14 ft from the center is traveling at 5 miles/hr. 4. a. If it takes 30 seconds to reach this speed, what is the angular acceleration of the carousel? b. What is the total acceleration of the rider at t = 30 seconds? An angled bracket rotates about a fixed shaft O. If the tangential acceleration and velocity of point B is 400 ft/s^2 and 60 ft/s, respectively, what is the total acceleration magnitude of point A?

Explanation / Answer

We are allowed to do 1 question at a time. Post again for second question.

2) a)

= 6t - 4

at t = 4

= 24 - 4 = 20

w = w0 + t

assuming w0 = 0 initially

w = 20 * t = 20 * 4 = 80 rad/s

b) w = 2* pi/T

T = 2*pi/w

T = 2 * 3.14/80

T for one revolution = 0.0785 s

T for 3 revolutions = 0.0785 * 3 = 0.2355 s

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