Problem 8: Penny is adjusting the position of a stand up piano of mass m, = 195 kg in her living room. The piano is , = 1.3 m in length. The piano is currently at an angle of 0, = 48 degrees to the wall. Penny wants to rotate the piano across the carpeted floor so that it is flat up against the wall. To move the piano, Penny pushes on it at the point furthest from the wall. This piano does not have wheels, so you can assume that the friction between the piano and the rug acts at the center of mass of the piano. 0, TTTTT| Randomized Variables т, 3D 195 kg , = 1.3 m 0, = 48 degrees Part (a) Write an expression for the minimum magnitude of the force F, in N Penny needs to exert on the piano to get it moving. Assume the corner of the piano on the wall doesn't slide and the static friction between the rug and the piano is u. Expression : Fs,min = Select from the variables below to write your expression. Note that all variables may not be required. a, B, us, 0, a, d, g, h, j, k, m„, n, P, S, t Part (b) The coefficient of kinetic friction between the carpet and the piano is u = 0.27. Once the piano starts moving, calculate the torque t, in N-m that Penny needs to apply to keep moving the piano at a constant angular velocity. Numeric : A numeric value is expected and not an expression. Tp = Part (c) Calculate the amount of work W, in J Penny does on the piano as she rotates it. Numeric : A numeric value is expected and not an expression. 281
Angular Momentum
The momentum of an object is given by multiplying its mass and velocity. Momentum is a property of any object that moves with mass. The only difference between angular momentum and linear momentum is that angular momentum deals with moving or spinning objects. A moving particle's linear momentum can be thought of as a measure of its linear motion. The force is proportional to the rate of change of linear momentum. Angular momentum is always directly proportional to mass. In rotational motion, the concept of angular momentum is often used. Since it is a conserved quantity—the total angular momentum of a closed system remains constant—it is a significant quantity in physics. To understand the concept of angular momentum first we need to understand a rigid body and its movement, a position vector that is used to specify the position of particles in space. A rigid body possesses motion it may be linear or rotational. Rotational motion plays important role in angular momentum.
Moment of a Force
The idea of moments is an important concept in physics. It arises from the fact that distance often plays an important part in the interaction of, or in determining the impact of forces on bodies. Moments are often described by their order [first, second, or higher order] based on the power to which the distance has to be raised to understand the phenomenon. Of particular note are the second-order moment of mass (Moment of Inertia) and moments of force.
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