Exam 10: Rotational Motion

A merry-go-round of radius R = 2.0 m has a moment of inertia I = 250 kg.m²,and is rotating at 10 rpm.A child whose mass is 25 kg jumps onto the edge of the merry-go-round,heading directly toward the center at 6.0 m/s.The new angular speed (in rpm)of the merry-go-round is approximately

A wheel rotating about a fixed axis with a constant angular acceleration of 2.0 rad/s² starts from rest at t = 0.The wheel has a diameter of 20 cm.What is the magnitude of the total linear acceleration of a point on the outer edge of the wheel at t = 0.60 s?

If L represents angular momentum,I represents moment of inertia,p represents linear momentum,m represents mass,and r represents a distance,which of the following can represent kinetic energy?

A disk (radius = 8.0 cm)that rotates about a fixed axis starts from rest and accelerates at a constant rate to an angular velocity of 4.0 rad/s in 2.0 s.What is the magnitude of the total linear acceleration of a point on the rim of the disk at the instant when the angular velocity of the disk is 1.5 rad/s?

A cylinder rotating about its axis with a constant angular acceleration of 1.6 rad/s² starts from rest at t = 0.At the instant when it has turned through 0.40 radian,what is the magnitude of the total linear acceleration of a point on the rim (radius = 13 cm)?

A pendulum bob of mass m is set into motion in a circular path in a horizontal plane as shown in the figure.The square of the angular momentum of the bob about the vertical axis through the point P is

A uniform cylinder of radius R,mass M,and length L rotates freely about a horizontal axis parallel and tangent to the cylinder,as shown below.The moment of inertia of the cylinder about this axis is

Three particles,each of which has a mass of 80 g,are positioned at the vertices of an equilateral triangle with sides of length 60 cm.The particles are connected by rods of negligible mass.What is the moment of inertia of this rigid body about an axis that is parallel to one side of the triangle and passes through the respective midpoints of the other two sides?

A horizontal disk with a radius of 10 cm rotates about a vertical axis through its center.The disk starts from rest at t = 0 and has a constant angular acceleration of 2.1 rad/s².At what value of t will the radial and tangential components of the linear acceleration of a point on the rim of the disk be equal in magnitude?

Four identical particles (mass of each = 0.40 kg)are placed at the vertices of a rectangle (2.5 m * 4.0 m)and held in those positions by four light rods which form the sides of the rectangle.What is the moment of inertia of this rigid body about an axis that passes through the mid-points of the shorter sides and is parallel to the longer sides?

Exhibit 10-1 The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track. Use this exhibit to answer the following question(s). -Refer to Exhibit 10-1.What is her angular displacement (in rad)in the first 12 minutes?

The figure below shows a graph of angular velocity as a function of time for a car driving around a circular track.Through how many radians does the car travel in the first 10 minutes?

The rigid body shown is rotated about an axis perpendicular to the paper and through the point P.If M = 0.40 kg,a = 30 cm,and b = 50 cm,how much work is required to take the body from rest to an angular speed of 5.0 rad/s? Neglect the mass of the connecting rods and treat the masses as particles.

In the figure,a 1.6-kg weight swings in a vertical circle at the end of a string having negligible weight.The string is 2 m long.If the weight is released with zero initial velocity from a horizontal position,its angular momentum (in kg.m²/s)at the lowest point of its path relative to the center of the circle is approximately

Exhibit 10-3 The graph below shows a plot of angular velocity in rad/s versus time in s from t = 0 s to t = 7 s. Use this exhibit to answer the following question(s). -Refer to Exhibit 10-3.The change in angular position, $\Delta$$\theta$ ,during the 7-second period is

A horizontal force of magnitude 6.5 N is exerted tangentially on a Frisbee of mass 32 grams and radius 14.3 cm.Assuming the Frisbee,a uniform disk,is originally at rest and the force is exerted for 0.08 s,determine the angular velocity of rotation about the central axis when the Frisbee is released.

A particle located at the position vector $\hat { \mathbf { r } } = ( \tilde { \mathbf { i } } + \hat { \mathbf { j } } )$ m has a force $\overrightarrow { \mathbf { F } } = ( 2 \hat { \mathbf { i } } + 3 \tilde { \mathbf { j } } )$ N acting on it.The torque about the origin is

Two vectors lying in the xz plane are given by the equations $\overrightarrow { \mathbf { A } } = 2 \tilde { \mathbf { i } } + 3 \tilde { \mathbf { k } }$ and $\overrightarrow { \mathbf { B } } = - \tilde { \mathbf { i } } + 2 \tilde { \mathbf { k } }$ .The value of $\overrightarrow { \mathbf { A } } \times \overrightarrow { \mathbf { B } }$ is

A small sphere attached to a light rigid rod rotates about an axis perpendicular to and fixed to the other end of the rod.Relative to the positive direction of the axis of rotation,the angular positions of the sphere are negative,its angular velocity is negative,and its angular acceleration is negative.The sphere is

The rigid object shown is rotated about an axis perpendicular to the paper and through point P.The total kinetic energy of the object as it rotates is equal to 1.4 J.If M = 1.3 kg and L = 0.50 m,what is the angular velocity of the object? Neglect the mass of the connecting rods and treat the masses as particles.