Numerade

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Penny Riley

Numerade educator

If instead of the force F an actual mass m = 0.690 kg is hung from the string, find the angular acceleration of the cylinder. Hint: The tension in the string induces the torque in both this part and the first part. The tension is not equal to mg! If it were, the mass would not accelerate downward. Determine all of the forces acting on the mass, then apply Newton's second law and solve for the tension, and apply it to Newton's second law of rotational motion. How far does m travel downward between 0.630 s and 0.830 s after the motion begins? The cylinder is changed to one with the same mass and radius, but a different moment of inertia. Starting from rest, the mass now moves a distance 0.373 m in a time of 0.470 s. Find I_cm of the new cylinder.

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Supratim Pal

Numerade educator

A yoyo with a mass of m = 152 g is released from rest as shown in the figure. The inner radius of the yoyo is r = 2.28 cm, and the outer radius is R = 3.68 cm, and the moment of inertia about the axis perpendicular to the plane of the yoyo and passing through the center of mass is ICM = 8.50 x 10^-5 kgm^2. Determine the linear acceleration of the yoyo. Determine the angular acceleration of the yoyo. What is the weight of the yoyo? What is the tension in the rope? If a 1.30 m long section of the rope unwinds from the yoyo, then what will be the angular speed of the yoyo?

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Timothy James

Numerade educator

The mass of a star is 1.690×10^31 kg and it performs one rotation in 30.70 days. Find its new period (in days) if the diameter suddenly shrinks to 0.670 times its present size. Assume a uniform mass distribution before and after.

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Supratim Pal

Numerade educator

A small mass M attached to a string slides in a circle (x) on a frictionless horizontal table, with the force F providing the necessary tension (see figure). The force is then increased slowly and then maintained constant when M travels around in circle (y). The radius of circle (x) is twice the radius of circle (y).

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Supratim Pal

Numerade educator

A cylindrically symmetric wheel rotates rapidly around a long horizontal shaft. The shaft is supported near one end, at P. The system is illustrated above just as the shaft is directed along the +y-axis (P to A). Give the direction of each of the quantities listed at that time. The change in angular momentum ?L, in a small ?t. The angular velocity of precession, ?p. The torque on the wheel, ?. The angular momentum of the wheel, L.

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Penny Riley

Numerade educator

A metal wire is bent to the shape of a circular arc. The wire is shown in blue in the figure. The arc is centered around the origin. What is the x coordinate of the arc's center of the mass? Please, notice that the circular arc goes through grid intersection points.

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Penny Riley

Numerade educator

We originally had a circular pie. We ate some of it, but a portion is still left. The leftover pie is shown in blue in the figure. The pie is centered around the origin of the reference frame. What is the x coordinate of the pie's center of the mass? Please, notice that the circular arc goes through grid intersection points.

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Linda Winkler

Numerade educator

A uniform plate of height 1.760 m is cut in the form of a parabolic section. The lower boundary of the plate is defined by: y=1.550x^2. Find the distance from the rounded tip of the plate to the center of mass. The fact that it is uniform means that it has the same density throughout. Since it is two-dimensional, it is a surface density; mass divided by area.

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Ivan Kochetkov

Numerade educator

A 4.67 kg steel ball strikes a massive wall at 14.5 m/s at an angle of ? = 59.9 with respect to the plane of the wall. It bounces off with the same speed and angle as seen in the figure. If the ball is in contact with the wall for 0.107 s, what is the average force exerted on the ball by the wall?

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Saikat Chatterjee

Numerade educator

Recent studies have raised concern about 'heading' in youth soccer (i.e., hitting the ball with the head). A soccer player 'heads' a size 3 ball deflecting it by 45.0°, and keeps its speed of 13.00 m/s constant. A size 3 ball has a mass of approximately 2.000 kg. What is the magnitude of the impulse which the player must impart to the ball? If the player's head has a mass of 2.00 kg, what is the magnitude of the average acceleration of the player's head during the impact. Assume that over the brief time of the impact, 36.90 ms, the player's head can be treated separately from the player's body.

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Misha P.