A wheel rolls to the right along a horizontal surface, down a ramp, then continues along a lower horizontal surface. 1)Draw graphs for the wheel’s angular position, angular velocity, and angular acceleration as functions of time. 2)If the wheel continues to roll without slipping through an angular displacement ϴ, how could one determine the linear displacement of the wheel, x?
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A wheel rolls to the right along a horizontal surface, down a ramp, then continues along a lower horizontal
surface.
1)Draw graphs for the wheel’s angular position,
time.
2)If the wheel continues to roll without slipping through an
linear displacement of the wheel, x?
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- A solid, uniform, spherical boulder (I=(2/5) MR2) starts from rest and rolls down a 75.0 [m] hill, as shown at the figure at the right. The top half of the hill is rough enough to cause the boulder to roll without slipping, but thelower half is covered with ice and there is no friction. What is the translational speed of the boulder when it reaches the bottom of the hill?The Subparts to be solved D & E. The angular position of a rod varies as 23.7t2 radians from time t = 0. The rod has two beads on it as shown in the following figure, one at r1 = 15 cm from the rotation axis and the other at r2 = 42 cm from the rotation axis. (Note: figure may not be drawn to scale.) (a) What is the instantaneous angular velocity (in rad/s) of the rod at t = 7 s? (Indicate the direction with the sign of your answer. Round your answer to at least one decimal place.) rad/s (b) What is the angular acceleration (in rad/s2) of the rod at t = 7 s? (Indicate the direction with the sign of your answer.) rad/s2 (c) What are the tangential speeds of the beads (in m/s) at t = 7 s? vt, 1 = m/s vt, 2 = m/s (d) What are the tangential accelerations of the beads at t = 7 s? (Enter the magnitudes in m/s2.) at, 1 = m/s2 at, 2 = m/s2 (e) What are the centripetal accelerations of the beads at t = 7 s? (Enter the magnitudes in m/s2.) ac, 1 = m/s2 ac, 2 =…Moments of Semicircle For the semicircle of diameter a=2.1 in., compute the following: • The moment of inertia about an axis parallel to the x axes through the centroid. • The moment of inertia about the y-axis. The product of inertia about the origin. The moment of inertia about an axis parallel to the x-axes through the centroid. I = = The moment of inertia about the y axis. Iy The product of inertia about the origin. Ixy = in 4 in 4
- Up Left Right Down A spinning disk is rotating at a rate of 4 rad/s in the counterclockwise direction as shown in the figure. If the disk is speeding up at a rate of 4 rad/s2, what is the direction of the angular acceleration vector? right down re 1 left hen upImagine that you could see a wheel spinning while speeding up, so you know that the angular velocity is (answer choice 1) , and the angular acceleration is (answer choice 2). But if instead the wheel is spinning counter clockwise and slowing down, so you know that the angular velocity is (answer choice 3) , and the angular acceleration is (answer choice 4). answer choices: out of page (positive) or into page (negative)A solid sphere of radius R rolls without slipping in a trough of radius 5R as shown to the right. Answer the following questions: 5R, a. At what point(s) in the sphere's motion does it have zero R centripetal acceleration? What is the direction of the acceleration vector at this point? b. At what point(s) in the sphere's motion does it have zero tangential acceleration? What is the direction of the acceleration at this point? c. Explain why the period of the oscillation for the solid sphere is independent of the mass of the solid sphere.
- A disk is rotating on a horizontal axis as shown in the figure. Answer the following questions if you pull out at A and push in at B along the axis of the disk.What is the direction of the torque acting on the disk? What is the direction of the initial angular momentum vector for the disk? The applied torque causes the wheel's axis (or angular momentum vector) to move. From the front view, what is the direction of motion of the L vector? A disk is rotating on a vertical axis as shown in the figure. Answer the following questions if you push in at A and pull out at B along the axis of the disk. What is the direction of the torque acting on the disk? What is the direction of the initial angular momentum vector for the disk? The applied torque causes the wheel's axis (or angular momentum vector) to move. From the front view, what is the direction of motion of the L vector?Because 2? rad = 1 rev, the angular displacement in part (b) corresponds to 2.23 rev. In general, dividing the number of radians by 6 gives a good approximation to the number of revolutions, because 2? ~ 6.QUESTION If the angular acceleration were doubled for the same duration, by what factor would the angular displacement change? PRACTICE IT Use the worked example above to help you solve this problem. A compact disc rotates from rest up to an angular speed of 34.0 rad/s in a time of 0.889 s. (a) What is the angular acceleration of the disc, assuming the angular acceleration is uniform? rad/s2(b) Through what angle does the disc turn while coming up to speed? rad(c) If the radius of the disc is 4.45 cm, find the tangential speed of a microbe riding on the rim of the disc. m/s(d) What is the magnitude of the tangential acceleration of the microbe at the given time? m/s2 EXERCISEHINTS: GETTING STARTED | I'M STUCK! Use the values from PRACTICE IT to help you work this exercise.…