Use the following information for the next two problems: A car wheel has a diameter of 24 inches and rolls on the ground. A nail is stuck in the car wheel at the location of radians. It takes 10 seconds for the wheel to rotate 10 in the counter-clockwise direction. Write a function h(t) that describes the height of the nail from the ground as the wheel rotates over time.
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- A ball of radius R is rolling across a rough surface without slipping. What is the relationship between the angular speed w and the translational speed v? Select the correct answer Ov=w/R Ov=Rw O v = 1/w Ov=w Ov=R/w Image size: S M L Max +A wheel with thin spokes can be considered a hoop, where I=mr. A bicycle wheel has a mass of .35 kg with a radius of .30 m and is spinning at 25 rad/s in the positive direction. Brakes apply a force of friction of 15 N at the rim. We will consider the rim of the wheel to be on the very outside of the wheel. (Remember significant digits.) a.) What is the direction of the torque provided by the brakes (positive or negative) b.) What is the magnitude of the torque applied by the brakes? Nm c.) What is the moment of angular inertia of the wheel? kgm2 d.) What is the angular acceleration of the wheel? rad/s? e.) How far does the wheel travel (in radians) before coming to rest? rad f.) How long does this take? s g.) With faulty brakes, only 8 N can be applied. How long would it take to stop the wheel under these conditions? s MacBook ProA 3 kilogram solid sphere with a radius of 15 centimeters rolls without slipping down a rough incline with a 35 degree angle. If the sphere rolls from rest from a height of 45 centimeters, determine the sphere's translational speed at the bottom of the incline. Also, draw the free body diagram. Also see the attached picture that goes with the problem. Thank you.
- Please help me understand the concepts to work this practice problem out.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 =…MII-1 Consider a solid disk of mass M and radius R, which has a uniform density. a) The disk is rotated about an axis that goes through its center and is perpendicular to its face, as shown in the diagram below on the left. Find a formula for its moment of inertia. Your answer should be a symbolic expression that only depends on the variables M and R. Hint: you will need to divide the disk into infinitesimal mass elements (dm) and then perform the integral: r?dm b) Suppose the radius of the disk is 12.5 cm and the mass is 1.75 kg. Use the formula from part a) to calculate a numerical value for the moment of inertia, in kg m2. c) Now the axis of rotation is moved from the center of the disk to the end of the disk, as shown in the diagram below on the right. Find an expression for its moment of inertia. Hint: theorem. As before, your answer should only depend on the variables M and R. d) Suppose the radius of the disk is 12.5 cm and the mass is 1.75 kg. Use the formula from part c) to…
- An electric fan is turned off, and its angular velocity decreases uniformly from 450 rev/min to 220 rev/min in a time interval of length 4.50s. a) Find the angular acceleration α in revolutions per second per second. b) Find the number of revolutions made by the fan blades during the time that they are slowing down in Part A. c) How many more seconds are required for the fan to come to rest if the angular acceleration remains constant at the value calculated in Part A?Consider a phonograph with a diameter of 0.6 m and a rotational speed of 33 RPM. Answer the following questions. What is its radius in m?What is its rotational speed in rad/s?What is the tangential speed on the phonograph's outer edge in m/s?What is the tangential speed at the center of the phonograph in m/s?What is the tangential speed halfway out to the edge of the phonograph?A long, thin uniform rod of length 1.29m and mass 2.08kg is pivoted about a horizontal, frictionless pin passing through one end. The rod is released from one end in the vertical position. L y Pivot x At the instant the rod is horizontal, find its angular speed. Submit Answer Tries 0/10 At the instant the rod is horizontal, what is its angluar acceleration? Submit Answer Tries 0/10 At the instant the rod is horizontal, what is the magnitude of its x-component of acceleration at its centre of mass? Submit Answer Tries 0/10 At the instant the rod is horizontal, what is the magnitude of its Y-component of acceleration at its centre of mass? Submit Answer Tries 0/10