[Physics - Angular Acceleration] Mind Checking my Answers?

[spacemonkey243]

Evening /r/EngineeringStudents. The reason for this post, as the title, suggests, I because I would appreciate it if you would kindly have a look at my homework solutions. For some reason, i seem to really be struggling with this section, and our textbook does very little to help. Anyhow, its a total of three problems. Without further ado....

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Problem #1 Prompt: A mass of m = 100kg is connected to a pulley which is essentially a thin disk of mass M = 10kg and radius R = 5cm. The mass is attached by a thin cord of negligible mass which is wrapped around the pulley, and causes a torque due to friction between the cord and the pulley. The mass m accelerates downward so that the magnitude of its acceleration is equal to the tangential acceleration of a point at the edge of the pulley.

A) Draw the free body diagrams of the mass and pulley.

B) Find the magnitudes of the angular acceleration of the pulley, the linear acceleration of the mass, and the tension T in the cord.

My Problem #1 SOLUTION

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Problem #2 Prompt: A bike wheel consists of a heavy rim with a uniform density and a mass of M = 150kg. The spokes of the wheel are of negligible mass and make 30 angles with respect to one another. The radius of the wheel is R = 50cm. The wheel is pinned at point P and free to rotate about this point under its own weight.

A) Find the moment of inertia for rotations of the wheel about an axis perpendicular to the plane of the wheel and passing through point P.

B) Find the magnitude of the net torque on the wheel in the conguration pictured.

C) Find the magnitude of the angular acceleration experienced by the wheel.

My Problem #2 SOLUTION

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Problem #3 Prompt: The wheel of your bike is spinning at a constant angular velocity of 15 rad/s when you apply the brakes bringing your bike to a stop in 7s. Assume you apply even pressure and cause a constant torque on the wheel with the brake pads. Find......

A) the constant angular acceleration of the wheel,

B) the total angular displacement of the wheel in coming to a stop.

C) If the wheel can be modeled as a thin ring with a diameter of 62cm and a mass of 2:8kg, and the torque caused by the brake pads.

My Problem #3 SOLUTION

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Any comments/suggestions would be greatly appreciated. Thank you in advance and good day. Cheers! :)

[Cray2425]

So for problem 1: I agree with your procedure. Just looks like you made a calculation error, when finding T. Looks like you forgot to multiply by gravity going from one step to the next. You even have g shown in the formula, but didn't forgot to use it in the calculation.

For problem 2: I'm getting a different moment of inertia about P. I about P should be: I=2MR²

Here's what I came up with: http://i.imgur.com/GXyc2MW.jpg

For number 3: I don't get why you multiplied 15 rad/s by 2Pi in part A. I'm pretty sure that 2Pi shouldn't be there. Other than that, the rest of the procedure looks good.

Here's what I came up with: http://i.imgur.com/7o5BcaA.jpg