Calculate the moment of inertia for a uniform, solid cylinder (mass MM, radius R

Question

Calculate the moment of inertia for a uniform, solid cylinder (mass MM, radius RR) if the axis of rotation is tangent to the side of the cylinder as shown in the figure below.

1)

Calculate the moment of inertia in terms of MR2MR2. (Express your answer to three significant figures.)

A uniform, solid sphere of radius 4.00 cm and mass 2.00 kg starts with a translational speed of 2.00 m/s at the top of an inclined plane that is 1.00 m long and tilted at an angle of 20.0° with the horizontal. Assume the sphere rolls without slipping down the ramp.

1)

Calculate the final speed of a solid sphere. (Express your answer to three significant figures.)

msms

MR2MR2

A driver applies a horizontal force of 18.0 N (to the right) to the top of a steering wheel, as shown in figure below. The steering wheel has a radius of 16.5 cm and a moment of inertia of 0.0940 kg·m2.

1)

Calculate the angular acceleration of the steering wheel about the central axis. (Express your answer to three significant figures.)

rad/s2rads2

A torque wrench is used to tighten a nut on a bolt. The wrench is ll=22 cm long, and a force of 115 N is applied at the end of the wrench as shown in the figure below.

1)

Calculate the torque about the axis that passes through the bolt. (Express your answer to two significant figures.)

NmNm

Explanation / Answer

1) I = icm+mr^2 = mr^2/2+mr^2 = 3/2mr^2

2) from conservation of energy

1/2mu^2+mgh = 1/2mv^2+1/2iw^2

1/2mu^2+mgh = 1/2mv^2+1/2*2/5mv^2 = 7/10 mv^2

7/10 v^2 = u2/2+gh

v^2 = 5/7u^2+10gh/7

v = 2.765 m/s

3) torque = i*alpha

alpha = rf/i = 0.165*18/0.094 = 31.59 rad/s^2

4) torque = rfsontheta = 8.65 Nm

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